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Search: id:A136467
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| A136467 |
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Triangle T, read by rows, where column 0 of T^m equals C(m*2^(n-1), n) as n=0,1,2,3,..., for all m. |
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+0
8
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| 1, 1, 1, 1, 4, 1, 4, 32, 16, 1, 70, 848, 576, 64, 1, 4368, 75648, 62208, 9216, 256, 1, 906192, 22313216, 21169152, 3792896, 143360, 1024, 1, 621216192, 21827627008, 23212261376, 4793434112, 223215616, 2228224, 4096, 1, 1429702652400
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Column 0 of T^(n+1) = row n of square array A136462 defined by: A136462(n,k) = C((n+1)*2^(k-1), k); T^n denotes the n-th matrix power of this triangle T = A136467.
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FORMULA
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Diagonals: T(n+1,n) = 4^n; T(n+2,n) = (2^(n+1) + n-1)*8^n.
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EXAMPLE
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Triangle T begins:
1;
1, 1;
1, 4, 1;
4, 32, 16, 1;
70, 848, 576, 64, 1;
4368, 75648, 62208, 9216, 256, 1;
906192, 22313216, 21169152, 3792896, 143360, 1024, 1;
621216192, 21827627008, 23212261376, 4793434112, 223215616, 2228224, 4096, 1;
1429702652400, 71889350288384, 83889221697536, 19373156990976, 1055047811072, 13257146368, 34865152, 16384, 1; ...
Column 0 of T^m is given by: [T^m](n,0) = C(m*2^(n-1), n) for n>=0.
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PROGRAM
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(PARI) {T(n, k)=local(M=matrix(n+1, n+1, r, c, binomial(r*2^(c-2), c-1)), P); P=matrix(n+1, n+1, r, c, binomial((r+1)*2^(c-2), c-1)); (P~*M~^-1)[n+1, k+1]}
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CROSSREFS
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Cf. columns: A136465, A136468, A136469; A136470 (matrix square); A136462.
Sequence in context: A143461 A066808 A033918 this_sequence A079188 A076810 A061642
Adjacent sequences: A136464 A136465 A136466 this_sequence A136468 A136469 A136470
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Dec 31 2007
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