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Search: id:A155001
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| A155001 |
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a(n)=9*a(n-1)+72*a(n-2), n>2 ; a(0)=1, a(1)=1, a(2)=17 . |
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+0
2
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| 1, 1, 17, 225, 3249, 45441, 642897, 9057825, 127809009, 1802444481, 25424248977, 358594243425, 5057894117169, 71339832581121, 1006226869666257, 14192509772837025, 200180922571503729, 2823489006787799361
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The sequences A155001, A155000, A154999, A154997 and A154996 have a common form: a(0)=a(1)=1, a(2)=2b+1, a(n)=(b+1)*a(n-1)+b(b+1)*a(n-2), with b some constant. The generating function of these is (1-b*x-b^2*x^2)/(1-(b+1)*x-b*(1+b)*x^2). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 20 2009]
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FORMULA
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a(n+1)=Sum_{k, 0<=k<=n}A154929(n,k)*8^(n-k).
a(n)=(1/2)*{[(9/2)+(3/2)*sqrt(41)]^(n-1)+[(9/2)-(3/2)*sqrt(41)]^(n-1)}+(25/246)*sqrt(41)*{[(9/2)+(3/2)*sqrt(41)]^(n-1)-[(9/2)-(3/2)*sqrt(41)]^(n-1)+(8/9)*[C(2*n,n) mod 2], n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Jan 20 2009]
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MAPLE
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a[0] := 1: a[1] := 1: a[2] := 17: for n from 3 to 25 do a[n] := 9*a[n-1]+72*a[n-2] end do: seq(a[n], n = 0 .. 17); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 21 2009]
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CROSSREFS
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Sequence in context: A160398 A081044 A016227 this_sequence A012095 A140842 A087608
Adjacent sequences: A154998 A154999 A155000 this_sequence A155002 A155003 A155004
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KEYWORD
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nonn
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 18 2009
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EXTENSIONS
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Corrected by Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 21 2009
Corrected and extended by Emeric Deutsch (deutsch(AT)duke.poly.edu) and R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 21 2009
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