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Search: id:A099486
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| A099486 |
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Expansion of x/((1+x^2)(1-4x+x^2)). |
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+0
4
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| 0, 1, 4, 14, 52, 195, 728, 2716, 10136, 37829, 141180, 526890, 1966380, 7338631, 27388144, 102213944, 381467632, 1423656585, 5313158708, 19828978246, 74002754276, 276182038859, 1030725401160, 3846719565780, 14356152861960
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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A Chebyshev transform of the sequence 0,1,4,16.. which has with g.f. x/(1-4x). The image of G(x) under the Chebyshev transform is (1/(1+x^2))G(x/(1+x^2)).
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FORMULA
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a(n)=4a(n-1)-2a(n-2)+4a(n-3); a(n)=sum{k=0..n, cos(pi*(n-k)/2)((2+sqrt(3))^k-(2-sqrt(3))^k)/(2sqrt(3))}; a(n)=sum{k=0..floor(n/2), C(n-k, k)(-1)^n*(4^(n-2k)-0^(n-2k))/4}.
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CROSSREFS
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Cf. A099487, A099488.
Sequence in context: A149488 A058692 A165813 this_sequence A047033 A017947 A052710
Adjacent sequences: A099483 A099484 A099485 this_sequence A099487 A099488 A099489
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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), Oct 18 2004
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