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Partial sums of A298016.
1

%I #8 Jan 16 2018 02:52:10

%S 1,7,19,31,55,91,115,157,217,253,313,397,445,523,631,691,787,919,991,

%T 1105,1261,1345,1477,1657,1753,1903,2107,2215,2383,2611,2731,2917,

%U 3169,3301,3505,3781,3925,4147,4447,4603,4843,5167,5335,5593,5941,6121,6397,6769,6961,7255,7651,7855,8167,8587

%N Partial sums of A298016.

%H Colin Barker, <a href="/A298019/b298019.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,2,-2,0,-1,1).

%F From _Colin Barker_, Jan 16 2018: (Start)

%F G.f.: (1 + 6*x + 12*x^2 + 10*x^3 + 12*x^4 + 12*x^5 + x^6) / ((1 - x)^3*(1 + x + x^2)^2).

%F a(n) = a(n-1) + 2*a(n-3) - 2*a(n-4) - a(n-6) + a(n-7) for n>6.

%F (End)

%o (PARI) Vec((1 + 6*x + 12*x^2 + 10*x^3 + 12*x^4 + 12*x^5 + x^6) / ((1 - x)^3*(1 + x + x^2)^2) + O(x^80)) \\ _Colin Barker_, Jan 16 2018

%Y Cf. A298016.

%K nonn,easy

%O 0,2

%A Chaim Goodman-Strauss and _N. J. A. Sloane_, Jan 13 2018