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A118024
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Triangle T, read by rows, T(n,k) = T(n-k)*2^(k*(n-k)) such that column 0 of the matrix square of T equals column 0 of T shifted left: [T^2](n,k) = T(n-k+1,0)*2^(k*(n-k)) for n>=k>=0.
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2
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1, 1, 1, 2, 2, 1, 6, 8, 4, 1, 28, 48, 32, 8, 1, 216, 448, 384, 128, 16, 1, 2864, 6912, 7168, 3072, 512, 32, 1, 66656, 183296, 221184, 114688, 24576, 2048, 64, 1, 2760896, 8531968, 11730944, 7077888, 1835008, 196608, 8192, 128, 1, 205824384, 706789376
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Column 0 is A118025, where T(n,k) = A118025(n-k)*2^(k*(n-k)).
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FORMULA
| T(n,k) = A118025(n-k)*2^(k*(n-k)) for n>=k>=0.
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EXAMPLE
| Triangle T begins:
1;
1,1;
2,2,1;
6,8,4,1;
28,48,32,8,1;
216,448,384,128,16,1;
2864,6912,7168,3072,512,32,1;
66656,183296,221184,114688,24576,2048,64,1; ...
2760896,8531968,11730944,7077888,1835008,196608,8192,128,1; ...
Matrix square is given by [T^2](n,k) = T(n-k+1,0)*2^(k*(n-k)):
1;
2,1;
6,4,1;
28,24,8,1;
216,224,96,16,1;
2864,3456,1792,384,32,1; ...
so that column 0 of T^2 equals column 0 of T shift left 1 place.
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PROG
| (PARI) {T(n, k)=if(n<0|k>n, 0, if(n==k, 1, 2^k*sum(j=0, n-1, T(n-1, j)*T(j, k)); ))} - Paul D. Hanna (pauldhanna(AT)juno.com), Sep 25 2006
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CROSSREFS
| Cf. A118025 (column 0); A117401 (related triangle); A118022 (variant).
Cf. A123305.
Sequence in context: A135880 A077873 A123305 * A184184 A074297 A020824
Adjacent sequences: A118021 A118022 A118023 * A118025 A118026 A118027
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KEYWORD
| nonn,tabl
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Apr 10 2006
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