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Search: id:A106392
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| A106392 |
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Expansion of 1/(1-6*x+10*x^2). |
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+0
1
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| 1, 6, 26, 96, 316, 936, 2456, 5376, 7696, -7584, -122464, -658944, -2729024, -9784704, -31417984, -90660864, -229785344, -472103424, -534767104, 1512431616, 14422260736, 71409248256, 284232882176, 991304810496, 3105500041216, 8719952142336, 21264712441856, 40388753227776
(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/((1-3x)^2+x^2); a(n)=sum{k=0..floor(n/2), binomial(n-k, k)(-10)^k*6^(n-2k)}; a(n)=sum{k=0..floor((n+1)/2), binomial(n+1, 2k+1)(-1)^k*3^(n-2k)}.
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PROGRAM
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(Other) sage: [lucas_number1(n, 6, 10) for n in xrange(1, 29)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
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CROSSREFS
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Sequence in context: A036638 A036645 A000393 this_sequence A143132 A055589 A055420
Adjacent sequences: A106389 A106390 A106391 this_sequence A106393 A106394 A106395
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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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