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Search: id:A106393
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| A106393 |
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Expansion of 1/(1-8x+17x^2). |
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+0
1
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| 1, 8, 47, 240, 1121, 4888, 20047, 77280, 277441, 905768, 2529647, 4839120, -4291039, -116593352, -859799153, -4896306240, -24553864319, -113193708472, -488133974353, -1980778750800, -7547952442399, -26710380775592, -85367854683953, -228866364286560, -379677384665279
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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In general, the sequence with g.f. 1/(1-2r*x+(r^2+1)*x^2)=1/((1-r*x)^2+x^2) has a(n)=sum{k=0..floor(n/2), binomial(n-k,k)(r^2-1)^k*(2r)^(n-2k)}; a(n)=sum{k=0..floor((n+1)/2), binomial(n+1,2k+1)(-1)^k*r^(n-2k)}.
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FORMULA
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G.f.: 1/((1-4*x)^2+x^2); a(n)=sum{k=0..floor(n/2), binomial(n-k, k)(-17)^k*8^(n-2k)}; a(n)=sum{k=0..floor((n+1)/2), binomial(n+1, 2k+1)(-1)^k*4^(n-2k)}.
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CROSSREFS
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Adjacent sequences: A106390 A106391 A106392 this_sequence A106394 A106395 A106396
Sequence in context: A026983 A081279 A099110 this_sequence A139262 A029760 A026900
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KEYWORD
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easy,sign
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 01 2005
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