The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A242783 Number T(n,k) of permutations of [n] with exactly k (possibly overlapping) occurrences of the consecutive step pattern given by the binary expansion of n, where 1=up and 0=down; triangle T(n,k), n>=0, read by rows. 24
 1, 1, 2, 5, 1, 21, 3, 70, 50, 450, 270, 4326, 602, 99, 12, 1, 34944, 5376, 209863, 139714, 13303, 1573632, 1366016, 530432, 158720, 21824925, 15302031, 2715243, 74601, 302273664, 161855232, 14872704, 2854894485, 2600075865, 712988175, 59062275 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Sum_{k>0} k*T(n,k) = A249249(n). LINKS Alois P. Heinz, Rows n = 0..130, flattened EXAMPLE T(7,3) = 12 because 12 permutations of {1,2,3,4,5,6,7} have exactly 3 (possibly overlapping) occurrences of the consecutive step pattern up, up, up given by the binary expansion of 7 = 111_2: (1,2,3,4,5,7,6), (1,2,3,4,6,7,5), (1,2,3,5,6,7,4), (1,2,4,5,6,7,3), (1,3,4,5,6,7,2), (2,1,3,4,5,6,7), (2,3,4,5,6,7,1), (3,1,2,4,5,6,7), (4,1,2,3,5,6,7), (5,1,2,3,4,6,7), (6,1,2,3,4,5,7), (7,1,2,3,4,5,6). Triangle T(n,k) begins: : n\k :       0        1       2       3  4  ... +-----+------------------------------------ :  0  :       1; :  1  :       1;                             [row  1 of A008292] :  2  :       2;                             [row  2 of A008303] :  3  :       5,       1;                    [row  3 of A162975] :  4  :      21,       3;                    [row  4 of A242819] :  5  :      70,      50;                    [row  5 of A227884] :  6  :     450,     270;                    [row  6 of A242819] :  7  :    4326,     602,     99,     12, 1; [row  7 of A220183] :  8  :   34944,    5376;                    [row  8 of A242820] :  9  :  209863,  139714,  13303;            [row  9 of A230695] : 10  : 1573632, 1366016, 530432, 158720;    [row 10 of A230797] MAPLE T:= proc(n) option remember; local b, k, r, h;       k:= iquo(n, 2, 'r'); h:= 2^ilog2(n);       b:= proc(u, o, t) option remember; `if`(u+o=0, 1, expand(       add(b(u-j, o+j-1, irem(2*t,   h))*`if`(r=0 and t=k, x, 1), j=1..u)+       add(b(u+j-1, o-j, irem(2*t+1, h))*`if`(r=1 and t=k, x, 1), j=1..o)))       end: forget(b);       (p-> seq(coeff(p, x, i), i=0..degree(p)))(b(n, 0, 0))     end: seq(T(n), n=0..15); MATHEMATICA T[n_] := T[n] = Module[{b, k, r, h}, {k, r} = QuotientRemainder[n, 2]; h = 2^Floor[Log[2, n]]; b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1, Expand[ Sum[b[u - j, o + j - 1, Mod[2*t, h]]*If[r == 0 && t == k, x, 1], {j, 1, u}] + Sum[b[u + j - 1, o - j, Mod[2*t + 1, h]]*If[r == 1 && t == k, x, 1], {j, 1, o}]]]; Function[p, Table[Coefficient[p, x, i], {i, 0, Exponent[p, x]}]][b[n, 0, 0]]]; Table[T[n], {n, 0, 15}] // Flatten (* Jean-François Alcover, Feb 20 2016, after Alois P. Heinz *) CROSSREFS Column k=0-10 give: A242785, A246221, A246222, A246223, A246224, A246225, A246226, A246227, A246228, A246229, A243105. Row sums give A000142. Cf. A242784, A249249, A295987, A335308. Sequence in context: A120294 A186766 A047921 * A177250 A102786 A222637 Adjacent sequences:  A242780 A242781 A242782 * A242784 A242785 A242786 KEYWORD nonn,tabf,look AUTHOR Alois P. Heinz, May 22 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 27 17:15 EDT 2020. Contains 338035 sequences. (Running on oeis4.)