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Search: id:A099173
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| A099173 |
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Array T(k,n) read by diagonals: g.f. of k-th row x/(1-2x-(k-1)x^2). |
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+0
1
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| 0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 4, 4, 0, 1, 2, 5, 8, 5, 0, 1, 2, 6, 12, 16, 6, 0, 1, 2, 7, 16, 29, 32, 7, 0, 1, 2, 8, 20, 44, 70, 64, 8, 0, 1, 2, 9, 24, 61, 120, 169, 128, 9, 0, 1, 2, 10, 28, 80, 182, 328, 408, 256, 10, 0, 1, 2, 11, 32, 101, 256, 547, 896, 985, 512, 11, 0, 1
(list; graph; listen)
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OFFSET
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0,6
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LINKS
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R. Stephan, Prove or disprove. 100 Conjectures from the OEIS, #16.
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FORMULA
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T(k, n) = Sum{i=0..[n/2], k^i * C(n, 2i+1) }.
Recurrence: T(k, 0)=0, T(k, 1)=1, T(k, n) = 2T(k, n-1) + (k-1)T(k, n-2).
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EXAMPLE
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0,1,2,3,4,5,6,
0,1,2,4,8,16,32,
0,1,2,5,12,29,70,
0,1,2,6,16,44,120,
0,1,2,7,20,61,182,
0,1,2,8,24,80,256,
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PROGRAM
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(PARI) T(k, n)=sum(i=0, n\2, k^i*binomial(n, 2*i+1))
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CROSSREFS
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Rows 0-12 are A001477, A000079, A000129, A002605, A015518, A063727, A002532, A083099, A015519, A003683, A002534, A083102, A015520, A091914.
Columns 0-4 are A000004, A000012, A009056, A008586.
Sequence in context: A025675 A025682 A025691 this_sequence A159880 A108456 A089107
Adjacent sequences: A099170 A099171 A099172 this_sequence A099174 A099175 A099176
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan, Oct 13 2004
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