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Search: id:A098526
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| A098526 |
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Expansion of (1+4x^2)/(1-x-16x^5). |
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+0
1
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| 1, 1, 5, 5, 5, 21, 37, 117, 197, 277, 613, 1205, 3077, 6229, 10661, 20469, 39749, 88981, 188645, 359221, 686725, 1322709, 2746405, 5764725, 11512261, 22499861, 43663205, 87605685, 179841285, 364037461, 724035237, 1422646517, 2824337477
(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)+16a(n-5); a(n)=sum{k=0..floor(n/2), binomial(n-2k, floor(k/2))4^k}.
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CROSSREFS
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Adjacent sequences: A098523 A098524 A098525 this_sequence A098527 A098528 A098529
Sequence in context: A119991 A131286 A013607 this_sequence A019162 A024951 A092519
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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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