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A110111
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Sequence associated to the recurrence b(n)=b(n-1)+3*b(n-2).
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1
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0, 1, 7, 133, 1330, 18430, 210490, 2673223, 31940881, 394918819, 4788779380, 58709030380, 715296121540, 8745656280829, 106717441265323, 1303667366328817, 15915556720909510, 194371775990116810
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| In general, let b(n) be the solution to b(n)=b(n-1)+k*b(n-2) with b(0)=0, b(1)=1. Then a(n)=b(n)b(n+1)b(n+2)/(k+1) has g.f. x/((1+kx-k^3*x^2)(1-(3k+1)x-k^3*x^2)).
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FORMULA
| G.f.: x/((1+3x-27x^2)(1-10x-27x^2)); a(n)=7a(n-1)+84a(n-2)-189a(n-3)-729a(n-4); a(n)=b(n)b(n+1)b(n+2)/4 where b(n)=(1/2+sqrt(13/2)^n/sqrt(13)-(1/2-sqrt(13)/2)/sqrt(13); a(n)=A006130(n-1)*A006130(n)*A006130(n+1)/4.
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CROSSREFS
| Sequence in context: A028420 A051832 A103050 * A082164 A119670 A003374
Adjacent sequences: A110108 A110109 A110110 * A110112 A110113 A110114
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jul 12 2005
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