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Search: id:A099787
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| A099787 |
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Sum C(n-k,3k)2^k*3^(n-4k), k=0..floor(n/4). |
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+0
3
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| 1, 3, 9, 27, 83, 267, 909, 3267, 12235, 46983, 182529, 711099, 2764619, 10704147, 41257341, 158371011, 605932099, 2312728095, 8812918161, 33549513579, 127652354627, 485608571547, 1847326271949, 7028217617859, 26742885359131
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OFFSET
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0,2
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COMMENT
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In general a(n)=sum{k=0..floor(n/4), C(n-k,3k)u^k*v^(n-4k)} has g.f. (1-v*x)^2/((1-v*x)^3-u*x^4) and satisfies the recurrence a(n)==3v*a(n-1)-3v^2*a(n-2)+v^3*a(n-3)+u*a(n-4).
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FORMULA
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G.f.: (1-3x)^2/((1-3x)^3-2x^4); a(n)=9a(n-1)-27a(n-2)+27a(n-3)+2a(n-4).
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CROSSREFS
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Cf. A099786.
Adjacent sequences: A099784 A099785 A099786 this_sequence A099788 A099789 A099790
Sequence in context: A052917 A099786 A131428 this_sequence A113994 A029527 A121746
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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 26 2004
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