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%I #38 Mar 16 2015 09:42:34
%S 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,
%T 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,
%U 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
%N 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.
%C The partial sums of row n give the n-th row of the square array A255741.
%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%F T(n,1) = 1; for k > 1, T(n,k) = (n-1)*(n-2)^(A000120(k-1)-1) with n >= 1.
%e The corner of the square array with the first 16 terms of the first 12 rows looks like this:
%e -------------------------------------------------------------------------
%e A000007: 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
%e A255738: 1, 1, 1, 0, 1, 0, 0, 0 1, 0, 0, 0, 0, 0, 0, 0
%e A040000: 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2
%e A151787: 1, 3, 3, 6, 3, 6, 6, 12, 3, 6, 6, 12, 6, 12, 12, 24
%e A147582: 1, 4, 4, 12, 4, 12, 12, 36, 4, 12, 12, 36, 12, 36, 36, 108
%e A151789: 1, 5, 5, 20, 5, 20, 20, 80, 5, 20, 20, 80, 20, 80, 80, 320
%e A151779: 1, 6, 6, 30, 6, 30, 30, 150, 6, 30, 30, 150, 30, 150, 150, 750
%e A151791: 1, 7, 7, 42, 7, 42, 42, 252, 7, 42, 42, 252, 42, 252, 252, 1512
%e A151782: 1, 8, 8, 56, 8, 56, 56, 392, 8, 56, 56, 392, 56, 392, 392, 2744
%e A255743: 1, 9, 9, 72, 9, 72, 72, 576, 9, 72, 72, 576, 72, 576, 576, 4608
%e A255744: 1,10,10, 90,10, 90, 90, 810,10, 90, 90, 810, 90, 810, 810, 7290
%e A255745: 1,11,11,110,11,110,110,1100,11,110,110,1100,110,1100,1100,11000
%e ...
%o (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
%Y Cf. A000120, A255741.
%Y Rows 1-12: A000007, A255738, A040000, A151787, A147582, A151789, A151779, A151791, A151782, A255743, A255744, A255745.
%Y Column 1 is A000012.
%Y Columns 2^k+1, for k >=0: A011477.
%Y Columns 4, 6, 7, 10, 11, 13...: 0 together with A002378.
%K nonn,tabl
%O 1,8
%A _Omar E. Pol_, Mar 05 2015
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