User:Andrey Zabolotskiy

Андрей Заболотский, Andrei Zabolotskii.

Mathematician at the Open University, UK.

If I commented on your sequence draft, you replied, my answer is expected, but I don't answer for three days, please do not hesitate to wiki-mail me.

I write about the OEIS.

OEIS contributions, including:

• new sequences:
  • A276638, a relative of Ivan Neretin's A272727;
  • A290705, theta series of triamond (this structure actually arose in my research);
  • A348566 and A348567, related to sandpiles, also contributions to A256045, see also my Rust program that can find terms of that array and some other sequences related to sandpiles;
  • A281487 and A281488, negated sums over divisors of n (mentioned in N. J. A. Sloane's talk);
  • A359335, essentially the Pfaffian of skew-symmetric 2n × 2n matrix with entries i XOR j for i < j, i=1..2n, j=1..2n.
  • A293060-A293063, the crystallographic point groups, subperiodic groups, and space groups, non-magnetic and magnetic, with and without enantiomorphs. My little magnum opus;
  • A292515, related to Conway's notation for knots, together with contributions to A007022, A113204, A072552, A078666, and A078672;
  • A300782-A300784, A300651, A350871-A350872, number of distinct sublattices of various lattices, together with the major revision of the sublattices-related sequences such as A304182 and references therein, A145392, A145394, A159842, A157230, A331143;
  • A352838 and A353091, walks with given algebraic area;
  • A361625, number of free polyominoes with checkerboard-pattern-colored vertices (inspired by the 3D version, A122675);
  • A360537, areas of certain Heron triangles related to Somos sequences;
  • A342811 and A342812, volume of certain permutohedra and associahedra;
  • A293237 and A293238, escape probabilities for a random walk on fcc, bcc, hcp, and diamond lattices;
  • A279903, Hausdorff dimension of E_{1,2} (also extension of A052483);
  • A282137, a linear recurrence related to the Khmelnik representation of integers, A066321 (also contributions to A320283);
  • A336877 and A336878, the harmonic function on the Sierpiński gasket;
  • A336398, rational knots;
  • A279402-A279409, independence and domination numbers for toroidal chess graphs, also A321684, A342576; contributions to other chess-related graph-theoretical sequences;
  • A288535-A288537, generalization of Conway's RATS to other bases;
  • A273619, leading digit of k in base n (needed for future sequences);
  • A277054-A277059, connections between repunits and pandigitals, together with Altug Alkan (also A282429);
  • A341630, polyiamonds;
  • A332342 and A332343, continued fractions meet algebra;
  • A274137, МЩ;
  • A273975, a 3D array: expansion of ((x^k−1)/(x−1))ⁿ;
• contributions to miscellaneous nice sequences invented by other people (this list not only shows my contributions, which are often minor, but also shows what sequences I consider really nice or useful):
  • A275302-A275305, related to Langton's ant on triangular lattice, by my pupil Oleg Nikulin;
  • A275667, cellular automaton on triangular tiling, by my pupil Alexey Kovba;
  • corrections and extensions from external sources for sequences related to counting knots and links such as A002863 and A049344;
  • programs for Conway's enumeration of rational knots A122495 and links A173637 (also extension of A018240, contributions to A277740);
  • nested log formula for A278813, A278452, and related sequences;
  • a program for A277795, Equisetum-like graphs;
  • corrections and program for A267794, relative of van Eck's sequence;
  • some terms and an asymptotic formula for A277828, number of coin tosses to get a run of consecutive identical result with probability >1/2;
  • exact programs for A291259 and A123690 together with Andres Cicuttin;
  • program for A355201, one of Tom Copeland's partition-indexed sequences;
  • contributions to sequences related to Lyndon words and irreducible polynomials such as A074446;
  • realizing that A132101 is a 1D analog of A250001;
  • contributions to A282390, the tripling polyominoes;
  • contribution to A089618, „a Khinchin sequence“;
  • contribution to A368052, related to Somos sequences;
  • an observation about A334444, related to the Lights Out puzzle, which inspired Problem 92.2 in Irish Math. Soc. Bulletin;
  • a term for A283075, times measurable by burning ropes;
  • program for A093914, the curling number of the Thue-Morse sequence;
  • program for A287150, the fairest turn sequence for 3 players, which is in some sense a generalization of the Thue-Morse sequence;
  • a simple formula connecting A335358 and A335359, the coordinates of the points of the Koch polyline, conjectured by me and later refined and proved by my pupil Artem Litvinov;
  • illustration for A003442, rooted dissections of n-gon;
  • corrections, programs, extensions for A112410 and related sequences, carbon skeletons with rings;
  • minor corrections to sequences related to the functional equation a(a(x)) = exp(x) − 1, see A052104;
  • extension and cleanup in A164950 related to the Sprouts game;
  • contributions to A278566, related to monstrous moonshine;
  • contributions to sequences counting „chemically relevant“ graphs such as A215622 or A167227;
  • contributions to other sequences related to chemistry and polyhex counting such as A038142, A253927, A121180, A120540;
  • a formula for A006082, number of flat trees;
  • contributions to A296516, the number of terms in a recursively defined polynomial;
  • contributions to A228369 and A296772, the compositions of integers (see also below), also to A048793, subsets of natural numbers;
  • contribution to A001998 (I found this sequence when counted by how many ways can we stack n layers of graphene commensurately);
  • correction to A091159, nets for n-hypercube;
  • corrections and extensions from literature and databases to sequences counting lattice polytopes such as A127709, A187015, or A105231;
  • contributions to sequences counting lattices and related objects such as A097584 or A054907, see also the mention of the space groups below;
  • updates to A191783, counting differentiable structures on n-sphere, and related sequences;
  • corrections to the table of maximal lattice densities in A093825;
  • more terms for sequences A005368 and A259976 related to representations of some permutation groups;
  • formulas and corrections for A117966 and A244042 and a program for A059095, related to the balanced ternary representation of integers;
  • a comment for A108918, reversed binary words in reversed lexicographic order, and observations about A118319, the inverse permutation;
  • extensions from literature for sequences counting algebraic systems such as A127707 and A181769;
  • contributions to A153036, related to the Stern-Brocot tree;
  • clarifications and extensions for Madelung constants such as A085469 and A182566;
  • expression for the exotic continued fraction A229555, highlighting the relation to 163;
  • clarifications for A242674 and A246665, constants related to the secretary problem;
  • contributions to A146978, related to the Rudvalis group;
  • extension of A318271, the Bridge and Torch problem;
  • contributions to Zorach additive triangle A035312 and related sequences, including A136561;
  • contributions to A074031-A074035 and other sequences related to irreducible polynomials over GF(4);
  • investigation of A280984, guarding dominoes problem;
  • combinatorial interpretation for A302335 and A302336, related to cycles in a grid;
  • program for A189226, curvatures in an Apollonian circle packing;
  • program (adopted from Marco Riedel's) for A309116, „cographs“;
  • contributions to theta series such as A217511;
  • contributions to A358653, cogrowth sequence of braid group;
  • corrections and extensions to sequences counting shifted Schröder paths such as A201079;
  • a formula for A092275, counting intersection points of lines;
  • contributions to A171108 and other sequences of Severi degrees;
  • contributions to A274369 and other Langton's ant related sequences;
  • crossrefs for A341319, related to gerrymandering;
  • an extra term for A061628, and identifying not-so-obvious source of the data;
  • extra terms for A036984, counting covariants for binary forms;
  • comment explaining the link between a simple period 5 sequence A135352 to friezes and triangulations;
  • collecting rows, columns and diagonals of A000027 written as a table as crossrefs for A055998;
  • identifying the „hypertriangular lattice“ from A344126 as the lcy net;
  • updates to A218537, rigid regular polygons;
  • a comment relating the triangles A099238 and A329146;
  • minor contributions to A180603 related to Brillouin zones;
  • a b-file for A039926, random digits (sic!);
  • empirical connection between a shuffling and cyclotomic polynomials, noticed in an abandoned draft and added to A289386;
  • a conjectured relation between A220418 and the Zassenhaus formula;
  • various formulas discovered using OEIS explorer and the wonderful Sequence Machine;
  • interesting trivia: A051037 is related to bamboo, A074650 was thought to be related to DNA;
• physics:
  • I went through all sequences related to classification of n-dimensional space groups, including magnetic space groups, and contributed to some of them. This started from A006227(5), number of 5-dimensional space groups, and culminated in A293060-A293063 (see above);
  • removing heresy from A003673 and A005600, the fine-structure constant, as well as from other sequences (there was a relevant discussion related to A361150 at some point);
  • another formula for A260832, „numbers J̃₂(n)“, which actually arose in my research;
  • contributions to A019694, 2π/5, and other sequences in connection with the redefinition of SI;
  • I went through all decimal expansions of constants of nature I could find and fixed the offsets in several of them;
  • dropping excessive digits of constants of nature;
  • references, extensions from literature, and sometimes formulas for many old sequences related to thermodynamics (of Ising model and the like) such as A003200, A002170, A002913, or A010571, or (surprisingly) polyominoes, such as A216820;
  • a program for A110818 and A111100, related to Ginzburg-Landau vortices;
• preparing the list of matches between OEIS sequences and RCSR coordination sequences;
• editorial work:
  • routine, including especially reviewing, recycling, and fixing dead links;
  • making some places in the OEIS guidelines more clear and closer to the current practice;
  • killing (with keyword dead) many old incorrect sequences, merging duplicates;
  • editing of A054434, the Rubik's cube related sequence with unknown definition (I am particularly proud of solving this mystery);
  • a program and discussion of binary Barker codes A276690;
  • crossrefs between different versions of the same sequences, such as A035607 (coordination sequences for hypercubic lattices) and A066099 (compositions of integers);
  • discussion about the balance between chemical and mathematical definitions of A134818;
  • clarifications to A040004 and A287286, related to Waring's problem mod n (it took time to verify that the difference in one term only is not a mistake);
  • help with sequences from new authors such as A290772 (some cyclic Gray codes) and A292046 (related to Elias omega coding);
  • investigation of spherical curves (immersions) A264759 together with main contribution from Robert Coquereaux (and then Brendan McKay), also contributions to related A264761, A008985;
  • an explanatory comment to A220952, Knuth's base-5 twisted enumeration of the nonnegative integers;
  • subtle corrections to A180620 and A231100, legs of primitive Pythagorean triples;
  • a simpler definition to A072833 (probably equivalent to the old one, no difference in the known terms);
  • fruitless but interesting investigation of A049021, number of ways to dissect a rectangle;
  • fixes to PARI programs for many sequences related to binary quadratic forms;
  • comments about handling outdated content from star contributors in the discussion of A285357;
  • a comment about uninteresting conjectures in the discussion of A058077;
  • fixed unpaired brackets in names of about a thousand sequences;
  • removing inappropriate unkn keyword;
  • fixing confusing names of sequences and sometimes whole obsc or uned sequence entries, one of the most interesting examples being A135317 with conjectured connections to stripe enumeration;
  • fixing incorrect crossrefs;
• etc.

The primary mechanism of decision-making in the OEIS community is NJAS ex machina.

Beware of the imp!