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

0,2

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).

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).

Mathematica

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

Crossrefs

Sequence in context: A000630 A036538 A341407 * A018240 A090596 A355385

Adjacent sequences: A108739 A108740 A108741 * A108743 A108744 A108745

Keyword

easy,nonn

Author

Paul Barry, Jun 22 2005

Status

approved