A077946 Expansion of 1/(1 - x - 2*x^2 - 2*x^3).

1, 1, 3, 7, 15, 35, 79, 179, 407, 923, 2095, 4755, 10791, 24491, 55583, 126147, 286295, 649755, 1474639, 3346739, 7595527, 17238283, 39122815, 88790435, 201512631, 457339131, 1037945263, 2355648787, 5346217575, 12133405675, 27537138399, 62496384899, 141837473047

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• nonn
• easy

Comments

Discarding the first 1 = INVERT transform of [1,2,2,0,0,0,...]. - Gary W. Adamson, Feb 16 2010

Links

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

Crossrefs

Cf. A077970.

Programs

PARI

Vec(1/(1-x-2*x^2-2*x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Formula

a(n) = leftmost term in M^n * [1 0 0], where M = the 3X3 matrix [1 1 1 / 2 0 0 / 0 1 0]. a(n) = a(n-1) + 2*a(n-2) + 2*a(n-3). a(n)/a(n-1) tends to 2.26953084..., an eigenvalue of M and a root of the characteristic polynomial x^3 - x^2 - 2x - 2. a(6) = 79 = 35 + 2*15 + 2*7 = a(5) + 2*a(4) + 2*a(3). - Gary W. Adamson, Dec 21 2004