A108742 Row sums of a triangle related to the Jacobsthal polynomials.

1, 2, 3, 7, 12, 24, 45, 86, 164, 312, 595, 1133, 2159, 4113, 7836, 14929, 28442, 54187, 103235, 196680, 374708, 713881, 1360062, 2591144, 4936560, 9404967, 17918025, 34136815, 65036305, 123904968, 236059553, 449732674, 856815475, 1632375855

Offset: 0

Author

Paul Barry, Jun 22 2005

Keywords

• easy
• nonn

Comments

Row sums of A108756.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,2,0,-1).

Programs

Mathematica

LinearRecurrence[{1,2,0,-1},{1,2,3,7},40] (* Harvey P. Dale, Feb 21 2016 *)

Formula

G.f.: (1 + x - x^2)/(1 - x - 2*x^2 + x^4).

a(n) = a(n - 1) + 2*a(n - 2) - a(n - 4) for n >= 4.

a(n) = Sum_{0 <= k <= n} binomial(floor((n + k + 1)/2) + k, floor((n + k)/2) - k).