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A113988
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Triangle, read by rows, equal to the matrix square of A113983.
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7
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1, 2, 1, 4, 4, 1, 8, 12, 6, 1, 18, 36, 26, 8, 1, 46, 116, 108, 46, 10, 1, 136, 416, 468, 248, 72, 12, 1, 464, 1680, 2194, 1366, 480, 104, 14, 1, 1818, 7656, 11294, 7976, 3222, 828, 142, 16, 1, 8122, 39256, 64152, 50186, 22590, 6568, 1316, 186, 18, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| G.f.: A(x, y) = ( (1-x*y)*GF(A113983) - 1/(1-x) )/(x^2*y) (cf. A113983). T(n, 0) = T(n-2, 0) + T(n-1, 1) + 2.
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EXAMPLE
| Triangle begins:
1;
2,1;
4,4,1;
8,12,6,1;
18,36,26,8,1;
46,116,108,46,10,1;
136,416,468,248,72,12,1;
464,1680,2194,1366,480,104,14,1;
1818,7656,11294,7976,3222,828,142,16,1;
8122,39256,64152,50186,22590,6568,1316,186,18,1;
41076,225348,402072,342584,168296,53816,12056,1968,236,20,1; ...
Notice that T(n+1,0) = T(n,1) + T(n-1,0) + 2:
T(7,0) = 464 = T(6,1) + T(5,0) = 416 + 46 + 2;
T(8,0) = 1818 = T(7,1) + T(6,0) = 1680 + 136 + 2.
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PROG
| (PARI) {T(n, k)=local(A, B); A=Mat(1); for(m=2, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(i<3|j==1|j==i, B[i, j]=1, B[i, j]=A[i-1, j-1]+(A^2)[i-2, j-1] ); )); A=B); (A^2)[n+1, k+1]}
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CROSSREFS
| Cf. A113989 (column 0), A113990 (column 1), A113991 (column 2), A113992 (column 3); A113983, A113993.
Sequence in context: A134395 A038207 A065109 * A134308 A202710 A200965
Adjacent sequences: A113985 A113986 A113987 * A113989 A113990 A113991
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KEYWORD
| nonn,tabl
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Nov 12 2005
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