A255740 Square array read by antidiagonals upwards: T(n,1) = 1; for k > 1, T(n,k) = (n-1)*(n-2)^(A000120(k-1)-1) with n >= 1.

1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 2, 0, 0, 1, 4, 3, 2, 1, 0, 1, 5, 4, 6, 2, 0, 0, 1, 6, 5, 12, 3, 2, 0, 0, 1, 7, 6, 20, 4, 6, 2, 0, 0, 1, 8, 7, 30, 5, 12, 6, 2, 1, 0, 1, 9, 8, 42, 6, 20, 12, 12, 2, 0, 0, 1, 10, 9, 56, 7, 30, 20, 36, 3, 2, 0, 0, 1, 11, 10, 72, 8, 42, 30, 80, 4, 6, 2, 0, 0, 1, 12, 11, 90, 9, 56, 42, 150, 5, 12, 6, 2, 0, 0

Offset

1,8

Comments

The partial sums of row n give the n-th row of the square array A255741.

Links

Table of n, a(n) for n=1..105.

Index entries for sequences related to cellular automata

Formula

T(n,1) = 1; for k > 1, T(n,k) = (n-1)*(n-2)^(A000120(k-1)-1) with n >= 1.

Example

The corner of the square array with the first 16 terms of the first 12 rows looks like this:
-------------------------------------------------------------------------
A000007: 1, 0, 0,  0, 0,  0,  0,   0, 0,  0,  0,   0,  0,   0,   0,    0
A255738: 1, 1, 1,  0, 1,  0,  0,   0  1,  0,  0,   0,  0,   0,   0,    0
A040000: 1, 2, 2,  2, 2,  2,  2,   2, 2,  2,  2,   2,  2,   2,   2,    2
A151787: 1, 3, 3,  6, 3,  6,  6,  12, 3,  6,  6,  12,  6,  12,  12,   24
A147582: 1, 4, 4, 12, 4, 12, 12,  36, 4, 12, 12,  36, 12,  36,  36,  108
A151789: 1, 5, 5, 20, 5, 20, 20,  80, 5, 20, 20,  80, 20,  80,  80,  320
A151779: 1, 6, 6, 30, 6, 30, 30, 150, 6, 30, 30, 150, 30, 150, 150,  750
A151791: 1, 7, 7, 42, 7, 42, 42, 252, 7, 42, 42, 252, 42, 252, 252, 1512
A151782: 1, 8, 8, 56, 8, 56, 56, 392, 8, 56, 56, 392, 56, 392, 392, 2744
A255743: 1, 9, 9, 72, 9, 72, 72, 576, 9, 72, 72, 576, 72, 576, 576, 4608
A255744: 1,10,10, 90,10, 90, 90, 810,10, 90, 90, 810, 90, 810, 810, 7290
A255745: 1,11,11,110,11,110,110,1100,11,110,110,1100,110,1100,1100,11000
...

Prog

(PARI) tabl(nn) = {for (n=1, nn, for (k=1, nn, if (k==1, x = 1, x= (n-1)*(n-2)^(hammingweight(k-1)-1)); print1(x, ", "); ); print(); ); } \\ Michel Marcus, Mar 15 2015

Crossrefs

Cf. A000120, A255741.

Rows 1-12: A000007, A255738, A040000, A151787, A147582, A151789, A151779, A151791, A151782, A255743, A255744, A255745.

Column 1 is A000012.

Columns 2^k+1, for k >=0: A011477.

Columns 4, 6, 7, 10, 11, 13...: 0 together with A002378.

Sequence in context: A171963 A357928 A292131 * A100995 A319273 A329615

Adjacent sequences: A255737 A255738 A255739 * A255741 A255742 A255743

Keyword

nonn,tabl

Author

Omar E. Pol, Mar 05 2015

Status

approved