A226638 Product of Pell and Lucas numbers.

0, 1, 6, 20, 84, 319, 1260, 4901, 19176, 74860, 292494, 1142459, 4462920, 17433181, 68099226, 266014100, 1039126224, 4059116419, 15856045380, 61938144041, 241947712356, 945115407340, 3691885043874, 14421535219799, 56334548849040, 220058498917081

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (2,7,2,-1).

Formula

Recurrence: a(n) = 2a(n-1) + 7a(n-2) + 2a(n-3) - a(n-4), n>3, starting 0,1,6,20.

G.f.: x*(x^2 + 4*x + 1)/(x^4 - 2*x^3 - 7*x^2 - 2*x + 1).

a(n) = A000129(n) * A000032(n).

Mathematica

LinearRecurrence[{2, 7, 2, -1}, {0, 1, 6, 20}, 30] (* Harvey P. Dale, Sep 26 2016 *)

Prog

(PARI) pell(n)=if(n<2, n>0, 2*pell(n-1)+pell(n-2))
lucas(n)=if(n<1, 2*(n>=0), fibonacci(n-1)+fibonacci(n+1))
a(n)=pell(n)*lucas(n)
(PARI) concat([0], Vec(x*(x^2+4*x+1)/(x^4-2*x^3-7*x^2-2*x+1)+O(x^66))) \\ Joerg Arndt, Sep 01 2013

Crossrefs

Sequence in context: A118265 A204271 A255469 * A274071 A246036 A151485

Adjacent sequences: A226635 A226636 A226637 * A226639 A226640 A226641

Keyword

nonn,easy

Author

Ralf Stephan, Sep 01 2013

Status

approved