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Search: id:A102320
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| A102320 |
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Triangular matrix, read by rows, that satisfies: T(n,k) = [T^2](n-1,k) when n>k>=0, with T(n,n) = (2*n+1). |
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+0
4
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| 1, 1, 3, 4, 9, 5, 33, 72, 25, 7, 436, 945, 300, 49, 9, 8122, 17568, 5425, 784, 81, 11, 197920, 427770, 130700, 18081, 1620, 121, 13, 6007205, 12979080, 3947050, 535864, 45441, 2904, 169, 15, 219413116, 473981445, 143812400, 19348042, 1599588, 95953
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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Column 0 forms A102321. Column 1 forms A102322. The contribution of each term along the main diagonal to column 0 is given by triangle of coefficients A102323.
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EXAMPLE
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Rows of T begin:
[1],
[1,3],
[4,9,5],
[33,72,25,7],
[436,945,300,49,9],
[8122,17568,5425,784,81,11],
[197920,427770,130700,18081,1620,121,13],
[6007205,12979080,3947050,535864,45441,2904,169,15],...
Matrix square T^2 equals T excluding the main diagonal:
[1],
[4,9],
[33,72,25],
[436,945,300,49],
[8122,17568,5425,784,81],...
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PROGRAM
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(PARI) {T(n, k)=local(A=Mat(1), B); for(m=2, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i, B[i, j]=2*j-1, if(j==1, B[i, j]=(A^2)[i-1, 1], B[i, j]=(A^2)[i-1, j])); )); A=B); return(A[n+1, k+1])}
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CROSSREFS
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Cf. A102086, A102321, A102322, A102323.
Sequence in context: A070154 A140439 A023183 this_sequence A021290 A016656 A084425
Adjacent sequences: A102317 A102318 A102319 this_sequence A102321 A102322 A102323
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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), Jan 05 2005
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