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Search: id:A073383
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| A073383 |
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Sixth convolution of A000129(n+1) (generalized (2,1)-Fibonacci, called Pell numbers), n>=0, with itself. |
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+0
2
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| 1, 14, 119, 784, 4396, 22008, 101220, 435696, 1777986, 6943244, 26129950, 95282992, 338108876, 1171554776, 3975215844, 13239402960, 43364985867, 139925413866, 445409413421, 1400429394784, 4353771487912
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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a(n)=sum(b(k)*c(n-k), k=0..n) with b(k) := A000129(k+1) and c(k) := A073382(k).
a(n)=sum((2^n)*binomial(n-k+6, 6)*binomial(n-k, k)*(1/4)^k, k=0..floor(n/2)).
a(n)= (7*(173205+212028*n+96812*n^2+20728*n^3+2092*n^4+80*n^5)*(n+1)*U(n+1)+(262125+435150*n+232364*n^2+54548*n^3+5836*n^4+232*n^5)*(n+2)*U(n))/(6!*8^4), with U(n) := A000129(n+1), n>=0.
G.f.: 1/(1-(2+x)*x)^7.
a(n)=F''''''(n+7, 2)/6!, that is, 1/6! times the 6th derivative of the (n+7)th Fibonacci polynomial evaluated at x=2. - T. D. Noe (noe(AT)sspectra.com), Jan 19 2006
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CROSSREFS
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Seventh (m=6) column of triangle A054456, A073382.
Adjacent sequences: A073380 A073381 A073382 this_sequence A073384 A073385 A073386
Sequence in context: A006223 A091303 A023012 this_sequence A022642 A004312 A002056
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Aug 2, 2002
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