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Search: id:A098524
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| A098524 |
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Expansion of (1+2x^2)/(1-x-4x^5). |
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+0
2
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| 1, 1, 3, 3, 3, 7, 11, 23, 35, 47, 75, 119, 211, 351, 539, 839, 1315, 2159, 3563, 5719, 9075, 14335, 22971, 37223, 60099, 96399, 153739, 245623, 394515, 634911, 1020507, 1635463, 2617955, 4196015, 6735659, 10817687, 17359539, 27831359, 44615419
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The expansion of (1+kx^2)/(1-x-k^2*x^5) satisfies the recurrence a(n)=a(n-1)+k^2*a(n-5),a(0)=1,a(1)=1,a(2)=k+1,a(3)=k+1,a(4)=k+1, with a(n)=sum{k=0..floor(n/2), binomial(n-2k,floor(k/2))r^k}.
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FORMULA
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a(n)=a(n-1)+4a(n-5); a(n)=sum{k=0..floor(n/2), binomial(n-2k, floor(k/2))2^k}.
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CROSSREFS
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Adjacent sequences: A098521 A098522 A098523 this_sequence A098525 A098526 A098527
Sequence in context: A031503 A049500 A137438 this_sequence A107709 A111521 A029628
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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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