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# User:Andrey Zabolotskiy

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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.

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); - 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;
- 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}}; - 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;
- 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“;
- 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;
- 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 A105232;
- contributions to sequences counting lattices and related objects such as A097584 or A054907, see also the mention of the space groups below;
- 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 for A085469 (also A108778), A181152, and A182566, the Madelung constants;
- 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;
- contributions to theta series such as A217511;
- 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;
- 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;
- 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;
- another formula for A260832, „numbers
*J̃*_{2}(*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 such as A002907, A003200, A001393, or A010571, or (surprisingly) polyominoes, such as A216820;

- 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 A264759 together with main contribution from Robert Coquereaux;
- 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); - 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;
- removing inappropriate
`unkn`keyword; - fixing confusing names of sequences and sometimes whole
`obsc`sequence entries: compare A162997 before and after; - fixing incorrect crossrefs;
- removing email addresses of deceased contributors;

- etc.

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