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Search: id:A099487
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| A099487 |
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Expansion of (1-3x+x^2)/((1+x^2)(1-4x+x^2)). |
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+0
4
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| 1, 1, 3, 14, 53, 195, 727, 2716, 10137, 37829, 141179, 526890, 1966381, 7338631, 27388143, 102213944, 381467633, 1423656585, 5313158707, 19828978246, 74002754277, 276182038859, 1030725401159, 3846719565780, 14356152861961
(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 1,1,4,16.. which has with g.f. (1-3x)/(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..floor(n/2), C(n-k, k)(-1)^n*(4^(n-2k)+3*0^(n-2k))/4}.
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CROSSREFS
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Cf. A099486, A099488.
Adjacent sequences: A099484 A099485 A099486 this_sequence A099488 A099489 A099490
Sequence in context: A105331 A017946 A083424 this_sequence A104191 A026544 A026527
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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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