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Search: id:A096591
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| A096591 |
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Triangle T, read by rows, such that the matrix square shifts T one place diagonally left and upward, with T(n,0)=T(n,n)=1 for n>=0. |
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3
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| 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 5, 5, 2, 1, 1, 1, 8, 10, 5, 2, 1, 1, 1, 15, 22, 14, 5, 2, 1, 1, 1, 28, 47, 34, 14, 5, 2, 1, 1, 1, 61, 113, 88, 42, 14, 5, 2, 1, 1, 1, 133, 269, 223, 116, 42, 14, 5, 2, 1, 1, 1, 328, 705, 609, 333, 132, 42, 14, 5, 2, 1, 1, 1, 807, 1843, 1660
(list; table; graph; listen)
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OFFSET
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0,8
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COMMENT
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Column with index 1 forms the row sums shift right. The convergent of the rows in reverse order is the Catalan sequence (A000108).
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FORMULA
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T(n, k) = Sum_{i=0..n-1} T(n-2, i)*T(i, k-1) for n>1 and k>0; T(n, 0)=T(n, n)=1.
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EXAMPLE
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Rows begin:
[1],
[1,1],
[1,1,1],
[1,2,1,1],
[1,3,2,1,1],
[1,5,5,2,1,1],
[1,8,10,5,2,1,1],
[1,15,22,14,5,2,1,1],
[1,28,47,34,14,5,2,1,1],
[1,61,113,88,42,14,5,2,1,1],
[1,133,269,223,116,42,14,5,2,1,1],...
The matrix square of T is given by:
[1],
[2,1],
[3,2,1],
[5,5,2,1],
[8,10,5,2,1],
[15,22,14,5,2,1],
[28,47,34,14,5,2,1],
[61,113,88,42,14,5,2,1],
[133,269,223,116,42,14,5,2,1],...
which equals T shift one place diagonally left and upward.
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PROGRAM
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(PARI) T(n, k)=if(n<k|k<0, 0, if(n==k|k==0, 1, sum(i=0, n-1, T(n-2, i)*T(i, k-1)); ))
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CROSSREFS
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Cf. A096592, A000108.
Sequence in context: A119269 A129713 A096669 this_sequence A115568 A072909 A095691
Adjacent sequences: A096588 A096589 A096590 this_sequence A096592 A096593 A096594
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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), Jun 28 2004
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