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%I #26 May 31 2019 05:12:07
%S 1,2,3,7,12,24,45,86,164,312,595,1133,2159,4113,7836,14929,28442,
%T 54187,103235,196680,374708,713881,1360062,2591144,4936560,9404967,
%U 17918025,34136815,65036305,123904968,236059553,449732674,856815475,1632375855
%N Row sums of a triangle related to the Jacobsthal polynomials.
%C Row sums of A108756.
%H Harvey P. Dale, <a href="/A108742/b108742.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,0,-1).
%F G.f.: (1 + x - x^2)/(1 - x - 2*x^2 + x^4).
%F a(n) = a(n - 1) + 2*a(n - 2) - a(n - 4) for n >= 4.
%F a(n) = Sum_{0 <= k <= n} binomial(floor((n + k + 1)/2) + k, floor((n + k)/2) - k).
%t LinearRecurrence[{1,2,0,-1},{1,2,3,7},40] (* _Harvey P. Dale_, Feb 21 2016 *)
%K easy,nonn
%O 0,2
%A _Paul Barry_, Jun 22 2005
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