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Search: id:A073382
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| A073382 |
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Fifth 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, 12, 90, 532, 2709, 12432, 52808, 211248, 805374, 2951576, 10465476, 36079848, 121412942, 400054032, 1293997416, 4117416496, 12910964103, 39956039172, 122193599822, 369685154076, 1107503284923, 3288114790112
(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) := A073381(k).
a(n)=sum((2^n)*binomial(n-k+5, 5)*binomial(n-k, k)*(1/4)^k, k=0..floor(n/2)).
a(n)= ((50085+53006*n+19594*n^2+3016*n^3+164*n^4 )*(n+1)*U(n+1)+(11355+16336*n+7042*n^2+1184*n^3+68*n^4)*(n+2)*U(n))/(3*5*2^13), with U(n) := A000129(n+1), n>=0.
G.f.: 1/(1-(2+x)*x)^6.
a(n)=F'''''(n+6, 2)/5!, that is, 1/5! times the 5th derivative of the (n+6)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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Sixth (m=5) column of triangle A054456, A073381.
Sequence in context: A084485 A135158 A130072 this_sequence A036216 A022640 A090749
Adjacent sequences: A073379 A073380 A073381 this_sequence A073383 A073384 A073385
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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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