A128416 Expansion of (1-4x^2)/(1+4x+3x^2).

1, -4, 9, -24, 69, -204, 609, -1824, 5469, -16404, 49209, -147624, 442869, -1328604, 3985809, -11957424, 35872269, -107616804, 322850409, -968551224, 2905653669, -8716961004, 26150883009, -78452649024, 235357947069, -706073841204, 2118221523609

Offset

0,2

Comments

Diagonal sums of number triangle A128414.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (-4,-3).

Formula

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

For n > 1, |a(n)| = 3*(|a(n-1)| - 1). - Tamas Kalmar-Nagy (integers(AT)kalmarnagy.com), Sep 17 2010

From Colin Barker, Sep 21 2016: (Start)

a(n) = (-1)^n*(9+5*3^n)/6 for n>0.

a(n) = -4*a(n-1)-3*a(n-2) for n>2. (End)

Prog

(PARI) Vec((1-4*x^2)/(1+4*x+3*x^2) + O(x^30)) \\ Colin Barker, Sep 21 2016

Crossrefs

Cf. A128414.

Sequence in context: A077922 A081149 A059507 * A353978 A334656 A175121

Adjacent sequences: A128413 A128414 A128415 * A128417 A128418 A128419

Keyword

easy,sign

Author

Paul Barry, Mar 02 2007

Status

approved