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A141448
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Generalized Pell numbers P(n,5,5).
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0
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0, 1, 2, 5, 13, 34, 89, 232, 605, 1578, 4116, 10736, 28003, 73041, 190515, 496926, 1296147, 3380779, 8818187, 23000741, 59993521, 156482896, 408159020, 1064613385, 2776862948, 7242974718, 18892067685, 49276745441, 128530009618
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| P(n,2,2) and P(n,2,1) are in A000129. P(n,3,2) is A116413. P(n,3,1) and P(n,3,3)
are A077939. P(n,4,1,) and P(n,4,4) are A103142.
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LINKS
| E. Kilic, D. Tasci, , The generalized Binet formula, representation and sums of the generalizedorder-k Pell numbers, Taiwanese J of Math vol 10 no 6 (2006), 1661-1670.
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FORMULA
| a(n)=2*a(n-1)+a(n-2)+a(n-3)+a(n-4)+a(n-5). G.f.: x/(1-2x-x^2-x^3-x^4-x^5). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 28 2008]
a(n+1)=sum(k=1..n, sum(r=0..k, binomial(k,r)*2^(k-r)*sum(m=0..r,(sum(j=0..m, binomial(j,-r+n-m-k-j)*binomial(m,j)))*binomial(r,m)))), a(0)=0, a(1)=1. [From Vladimir Kruchinin kru(AT)ie.tusur.ru, May 05 2011]
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MAPLE
| P := proc(n, k, i) option remember ; if n = 1-i then 1; elif n <= 0 then 0; else 2*P(n-1, k, i)+add(P(n-j, k, i), j=2..k) ; fi ; end: for n from 0 to 40 do printf("%d, ", P(n, 5, 5)) ; od:
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PROG
| (Maxima)
a(n):=b(n+1);
b(n):=sum(sum(binomial(k, r)*2^(k-r)*sum((sum(binomial(j, -r+n-m-k-j)*binomial(m, j), j, 0, m))*binomial(r, m), m, 0, r), r, 0, k), k, 1, n); [From Vladimir Kruchinin kru(AT)ie.tusur.ru, May 05 2011]
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CROSSREFS
| Sequence in context: A103142 A112844 A027933 * A011783 A001519 A122367
Adjacent sequences: A141445 A141446 A141447 * A141449 A141450 A141451
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KEYWORD
| easy,nonn
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AUTHOR
| R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 07 2008
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