A124861 Expansion of 1/(1-x-3*x^2-4*x^3-2*x^4).

1, 1, 4, 11, 29, 80, 219, 597, 1632, 4459, 12181, 33280, 90923, 248405, 678656, 1854123, 5065557, 13839360, 37809835, 103298389, 282216448, 771029675, 2106492245, 5755043840, 15723072171, 42956232021, 117358608384, 320629680811, 875976578389, 2393212518400, 6538378193579

Offset: 0

Author

Paul Barry, Nov 10 2006

Keywords

• easy
• nonn

Comments

Diagonal sums of number triangle A124860.

Links

• Index entries for linear recurrences with constant coefficients, signature (1,3,4,2).

Programs

Mathematica

LinearRecurrence[{1,3,4,2},{1,1,4,11},30] (* or *) CoefficientList[ Series[ 1/(1-x-3x^2-4x^3-2x^4),{x,0,30}],x] (* Harvey P. Dale, Apr 22 2011 *)

PARI

Vec(1/(1-x-3*x^2-4*x^3-2*x^4) + O(x^40)) \\ Michel Marcus, May 19 2025

Formula

a(n) = a(n-1)+3*a(n-2)+4*a(n-3)+2*a(n-4); a(n) = Sum_{k=0..floor(n/2)} J(n-k+1)*C(n-k,k) where J(n) = A001045(n). - corrected by Harvey P. Dale, Apr 22 2011

G.f.: 1 + x/(G(0) - x) where G(k) = 1 - 8*x - 2*k*x + k + 2*x*(k+1)*(k+5)/G(k+1); (continued fraction). - Sergei N. Gladkovskii, Apr 09 2013

Extensions

More terms from Michel Marcus, May 19 2025