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Search: id:A073380
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| A073380 |
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Third 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, 8, 44, 200, 810, 3032, 10716, 36248, 118435, 376240, 1167720, 3553840, 10636180, 31375440, 91392040, 263266512, 750922021, 2123059448, 5955034740, 16584106040, 45884989054, 126202397032
(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) := A054457(k).
a(n)=sum((2^n)*binomial(n-k+3, 3)*binomial(n-k, k)*(1/4)^k, k=0..floor(n/2)).
a(n)= ((147+94*n+14*n^2)*(n+1)*U(n+1)+3*(15+12*n+2*n^2)*(n+2)*U(n))/(3*2^7), with U(n) := A000129(n+1), n>=0.
G.f.: 1/(1-(2+x)*x)^4.
a(n)=F'''(n+4, 2)/6, that is, 1/6 times the 3rd derivative of the (n+4)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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Fourth (m=3) column of triangle A054456, A054457 (m=2).
Sequence in context: A005798 A092877 A023007 this_sequence A022636 A003518 A100575
Adjacent sequences: A073377 A073378 A073379 this_sequence A073381 A073382 A073383
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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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