A108756 -id:A108756 - cp's OEIS frontend

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

Paul Barry, Jun 22 2005

Row sums of A108756.

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).

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

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).

A109220 Expansion of (1+x-x^2)/(1-2x-2x^2+x^4).

Original entry on oeis.org

1, 3, 7, 20, 53, 143, 385, 1036, 2789, 7507, 20207, 54392, 146409, 394095, 1060801, 2855400, 7685993, 20688691, 55688567, 149899116, 403489373, 1086088287, 2923466753, 7869210964, 21181866061, 57016065763, 153472396895

Offset: 0

Paul Barry, Jun 22 2005

Transform of 2^n under matrix A108756.

Index entries for linear recurrences with constant coefficients, signature (2,2,0,-1).

a(n)=2a(n-1)+2a(n-2)-a(n-4); a(n)=a(n)=sum{k=0..n, binomial(floor((n+k+1)/2)+k, floor((n+k)/2)-k)*2^k}.

cp's OEIS Frontend

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

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