A122910 Expansion of (1-2x-3x^2)/((1-2x)(1+4x)(1-8x)).

1, 4, 45, 302, 2636, 20184, 165040, 1305952, 10504896, 83809664, 671394560, 5367485952, 42954566656, 343577810944, 2748857364480, 21989919383552, 175923113148416, 1407369872769024, 11259019111628800, 90071912374730752

Offset: 0

Author

Paul Barry, Sep 18 2006

Keywords

• easy
• nonn

Comments

Let M be the matrix M(n,k)=J(k+1)*sum{j=0..n, (-1)^(n-j)C(n,j)C(j+1,k+1)}. a(n) gives the row sums of M^3.

Links

• Index entries for linear recurrences with constant coefficients, signature (6,24,-64).

Programs

Mathematica

CoefficientList[Series[(1-2x-3x^2)/((1-2x)(1+4x)(1-8x)),{x,0,30}],x] (* or *) LinearRecurrence[{6, 24, -64}, {1, 4, 45}, 30] (* Harvey P. Dale, Jun 21 2011 *)

Formula

G.f.: (1-2x-3x^2)/(1-6x-24x^2+64x^3); a(n)=5*8^n/8+7*(-4)^n/24+2^n/12; a(n)=J(n)*A083424(n-1)+J(n+1)*A083424(n) where J(n) are the Jacobsthal numbers A001045(n).

a(0)=1, a(1)=4, a(2)=45, a(n)=6*a(n-1)+24*a(n-2)-64*a(n-3). - Harvey P. Dale, Jun 21 2011