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Search: id:A054457
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| A054457 |
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Pell numbers A000129(n+1) (without P(0)) convoluted twice with itself. |
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+0
8
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| 1, 6, 27, 104, 366, 1212, 3842, 11784, 35223, 103122, 296805, 842160, 2360780, 6549240, 18004980, 49106992, 132996957, 357948894, 957993823, 2550977112, 6761742234, 17848312884, 46932923478, 122980461816
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n)= A054456(n+2,2) (third column of Pell convolution triangle).
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FORMULA
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a(n)= ((10*n^2+39*n+32)*P(n+1)+(n+1)*(4*n+11)*P(n))/32, P(n)=A000129(n).
G.f.: 1/(1-2*x-x^2)^3.
a(n)=F''(n+3, 2)/2, that is, 1/2 times the 2nd derivative of the (n+3)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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Cf. A054456, A000129, A006645.
Sequence in context: A027312 A057222 A124641 this_sequence A000395 A005325 A099623
Adjacent sequences: A054454 A054455 A054456 this_sequence A054458 A054459 A054460
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KEYWORD
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easy,nonn
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Apr 27 2000
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