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Search: id:A053088
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| 1, 0, 3, 2, 9, 12, 31, 54, 117, 224, 459, 906, 1825, 3636, 7287, 14558, 29133, 58248, 116515, 233010, 466041, 932060, 1864143, 3728262, 7456549, 14913072, 29826171, 59652314, 119304657, 238609284, 477218599, 954437166, 1908874365
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Growth of happy bug population in GCSE maths course work assignment.
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FORMULA
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G.f.: 1/(1-3x^2-2x^3).
With offset 1: a(1)=1; a(n)=2*a(n-1)-(-1)^n*n; a(n)=(1/9)*(2^(n+1)-(-1)^n*(3*n+2)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 02 2002
a(n)=sum{k=0..floor(n/2), A078008(n-2k)} - Paul Barry (pbarry(AT)wit.ie), Nov 24 2003
a(n)=sum{k=0..floor(n/2), binomial(k, n-2k)3^k*(2/3)^(n-2k)}. - Paul Barry (pbarry(AT)wit.ie), Oct 16 2004
a(n)=sum{k=0..n, A078008(k)(1-(-1)^(n+k-1))/2; - Paul Barry (pbarry(AT)wit.ie), Apr 16 2005
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CROSSREFS
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Sequence in context: A099887 A038220 A053151 this_sequence A077898 A076584 A049969
Adjacent sequences: A053085 A053086 A053087 this_sequence A053089 A053090 A053091
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KEYWORD
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nonn,easy
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AUTHOR
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Pauline Gorman (pauline(AT)gorman65.freeserve.co.uk), Feb 26 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Feb 28 2000 and Christian G. Bower (bowerc(AT)usa.net), Feb 29 2000.
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