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Search: id:A098527
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| A098527 |
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Expansion (1+x^3)/(1-x-x^7). |
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+0
1
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| 1, 1, 1, 2, 2, 2, 2, 3, 4, 5, 7, 9, 11, 13, 16, 20, 25, 32, 41, 52, 65, 81, 101, 126, 158, 199, 251, 316, 397, 498, 624, 782, 981, 1232, 1548, 1945, 2443, 3067, 3849, 4830, 6062, 7610, 9555, 11998, 15065, 18914, 23744, 29806, 37416, 46971, 58969, 74034, 92948
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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The expansion of (1+kx^2)/(1-x-k^2*x^7) satisfies the recurrence a(n)=a(n-1)+k^2*a(n-7),a(0)=1,a(1)=1,a(2)=1,a(3)=k+1,a(4)=k+1, a(5)=k+1,a(6)=k+1 with a(n)=sum{k=0..floor(n/3), binomial(n-3k,floor(k/2))r^k}.
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FORMULA
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a(n)=a(n-1)+a(n-7); a(n)=sum{k=0..floor(n/3), binomial(n-3k, floor(k/2))}.
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CROSSREFS
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Cf. A097333, A098523.
Sequence in context: A029101 A029080 A058360 this_sequence A035635 A029100 A098133
Adjacent sequences: A098524 A098525 A098526 this_sequence A098528 A098529 A098530
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Sep 12 2004
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