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A099432
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Convolution of A030195(n) (generalized (3,3)-Fibonacci) with itself.
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0
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1, 6, 33, 162, 756, 3402, 14931, 64314, 273051, 1145988, 4764744, 19656756, 80561061, 328316814, 1331513397, 5377120038, 21633427836, 86747114430, 346810621815, 1382826606210, 5500378861551, 21830478128136, 86469557676048
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| G.f.: 1/(1-3*x-3*x^2)^2.
a(n)=6*a(n-1)-3*a(n-2)-18*a(n-3)-9*a(n-4).
a(n)=sum{k=0..floor((n+2)/2), k*binomial(n-k+2, k)3^(n-k+1)}.
a(n)=(sqrt(7)n+2sqrt(7)-sqrt(3))(5sqrt(7)/98+sqrt(3)/14)(3sqrt(21)/2 + 15/2)^(n/2) +(15/2-3sqrt(21)/2)^(n/2)(sqrt(7)n+2sqrt(7)+sqrt(3))(5sqrt(7)/98-sqrt(3)/14)(-1)^n.
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MATHEMATICA
| LinearRecurrence[{6, -3, -18, -9}, {1, 6, 33, 162}, 30] (* From Harvey P. Dale, May 20 2011 *)
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CROSSREFS
| Cf. A073388.
Sequence in context: A120009 A074087 A022730 * A072260 A203155 A084153
Adjacent sequences: A099429 A099430 A099431 * A099433 A099434 A099435
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Oct 15 2004
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EXTENSIONS
| Second formula corrected by Harvey P. Dale, May 20 2011.
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