A093381 Expansion of (1 - 2*x - 3*x^2 - 4*x^3)/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)).

1, 8, 42, 186, 766, 3058, 12062, 47426, 186606, 735858, 2909182, 11528866, 45781646, 182104658, 725311902, 2891845506, 11539011886, 46070609458, 184025468222, 735329653346, 2938999333326, 11749034250258, 46975237266142

Offset: 0

Author

Paul Barry, Apr 28 2004

Keywords

• easy
• nonn

Comments

Second binomial transform of A093380.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (10,-35,50,-24).

Crossrefs

Cf. A033484.

Programs

Magma

[4/3-5*2^n+2*3^n+8*4^n/3: n in [0..30]]; // Vincenzo Librandi, May 31 2011

Mathematica

CoefficientList[Series[(1-2x-3x^2-4x^3)/((1-x)(1-2x)(1-3x)(1-4x)),{x,0,30}],x] (* or *) LinearRecurrence[{10,-35,50,-24},{1,8,42,186},30] (* Harvey P. Dale, May 29 2013 *)

Formula

a(n) = 4/3 - 5*2^n + 2*3^n + 8*4^n/3;

a(n) = 2*A000244(n) - 5*A000079(n) + 4*A001045(2n+1).

a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4), n > 3. - Harvey P. Dale, May 29 2013