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Search: id:A102225
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| A102225 |
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Triangular matrix, read by rows, where row k is formed from the first differences of row (k-1) of its matrix square, with an appended '1' for the main diagonal. |
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+0
6
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| 1, 1, 1, 2, -1, 1, 3, -5, 3, 1, 7, -20, 19, -5, 1, 17, -51, 57, -33, 11, 1, 75, -289, 438, -345, 143, -21, 1, 346, -1426, 2441, -2073, 767, -97, 43, 1, 4874, -22622, 44289, -46156, 26231, -7713, 1183, -85, 1, 49047, -259734, 530214, -520395, 272461, -103617, 30735, 1119, 171, 1, 3009094, -15968025, 35495592
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Row sums are: {1,2,2,2,2,2,...}. Column 0 is A102226. Column 1 is A102227. Matrix square forms A102228.
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FORMULA
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T(n, k) = [T^2](n-1, k) - [T^2](n-1, k-1) for n>k>0, with T(n, n)=1 for n>=0 and T(n, 0) = [T^2](n-1, 0) for n>0.
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EXAMPLE
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Rows begin:
[1],
[1,1],
[2,-1,1],
[3,-5,3,1],
[7,-20,19,-5,1],
[17,-51,57,-33,11,1],
[75,-289,438,-345,143,-21,1],
[346,-1426,2441,-2073,767,-97,43,1],
[4874,-22622,44289,-46156,26231,-7713,1183,-85,1],...
The matrix square A102225^2 forms A102228:
[1],
[2,1],
[3,-2,1],
[7,-13,6,1],
[17,-34,23,-10,1],
[75,-214,224,-121,22,1],...
The first differences of the rows of A102228
form A102225 excluding the main diagonal of 1's.
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PROGRAM
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(PARI) {T(n, k)=local(A=matrix(1, 1), B); A[1, 1]=1; for(m=2, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i, B[i, j]=1, if(j==1, B[i, 1]=(A^2)[i-1, 1], B[i, j]=(A^2)[i-1, j]-(A^2)[i-1, j-1])); )); A=B); return(A[n+1, k+1])}
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CROSSREFS
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Cf. A102226, A102227, A102228.
Sequence in context: A144866 A058732 A060082 this_sequence A145236 A075248 A128325
Adjacent sequences: A102222 A102223 A102224 this_sequence A102226 A102227 A102228
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KEYWORD
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sign,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jan 01 2005
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