A124280 Expansion of 1/(1-x-x^2+x^3-x^4).

1, 1, 2, 2, 4, 5, 9, 12, 20, 28, 45, 65, 102, 150, 232, 345, 529, 792, 1208, 1816, 2761, 4161, 6314, 9530, 14444, 21821, 33049, 49956, 75628, 114356, 173077, 261761, 396110, 599150, 906576, 1371377, 2074913, 3138864, 4748976, 7184304, 10869329, 16443521

Offset: 0

Author

Paul Barry, Oct 24 2006

Keywords

• easy
• nonn
• changed

Comments

Diagonal sums of number triangle A124279.

Links

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

Crossrefs

Cf. A124279.

Programs

Mathematica

CoefficientList[Series[1/(1-x-x^2+x^3-x^4),{x,0,37}],x] (* Stefano Spezia, Aug 25 2025 *)

Formula

a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..n-2k}, C(j,n-2k-j)*C(k,n-2k-j) for n > 0.

a(n) = a(n-1)+a(n-2)-a(n-3)+a(n-4) for n > 3. - Carl Najafi, May 06 2014