A124789 Expansion of (1+x^2)/(1-x^4-x^5).

1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 4, 4, 5, 7, 8, 8, 9, 12, 15, 16, 17, 21, 27, 31, 33, 38, 48, 58, 64, 71, 86, 106, 122, 135, 157, 192, 228, 257, 292, 349, 420, 485, 549, 641, 769, 905, 1034, 1190, 1410, 1674, 1939, 2224, 2600, 3084, 3613

Offset: 0

Author

Paul Barry, Nov 07 2006

Keywords

• easy
• nonn

Comments

Diagonal sums of A124788.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,1,1).

Crossrefs

Cf. A017827, A103372.

Programs

Mathematica

CoefficientList[Series[(1+x^2)/(1-x^4-x^5),{x,0,60}],x] (* or *) LinearRecurrence[ {0,0,0,1,1},{1,0,1,0,1},60] (* Harvey P. Dale, Aug 20 2013 *)

Formula

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

a(n) = A017827(n)+A017827(n-2). - R. J. Mathar, May 09 2013

a(n) = A103372(n-3) for n >= 4. - Georg Fischer, Nov 03 2018

a(n) = (-1)^n*A124746(n). - R. J. Mathar, Jun 30 2020