A228748 Pell numbers (A000129) minus Lucas numbers beginning at 2 (A000032).

-2, 0, -1, 1, 5, 18, 52, 140, 361, 909, 2255, 5542, 13538, 32940, 79939, 193661, 468625, 1133118, 2738432, 6615760, 15979301, 38589489, 93182755, 224994602, 543236038, 1311570360, 3166544519, 7644930841, 18456845405, 44559332298

Offset

0,1

Links

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (3,0,-3,-1).

Formula

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

G.f.: -(2*x^3+x^2-6*x+2) / ((x^2+x-1)*(x^2+2*x-1)). [Joerg Arndt, Sep 03 2013]

Example

a(0) = Pell(0) - L(0) = 0 - 2 = -2.
a(1) = Pell(1) - L(1) = 1 - 1 = 0.
a(8) = Pell(8) - L(8) = 408 - 47 = 361.

Prog

(PARI) Vec( -(2*x^3+x^2-6*x+2) / ((x^2+x-1)*(x^2+2*x-1)) +O(x^66) ) \\ Joerg Arndt, Sep 03 2013

Crossrefs

Cf. A000032, A000129, A060405, A226638.

Sequence in context: A243986 A322838 A085496 * A343464 A225094 A350594

Adjacent sequences: A228745 A228746 A228747 * A228749 A228750 A228751

Keyword

sign,easy

Author

Jonathan Vos Post, Sep 02 2013

Status

approved