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A298032 Partial sums of A298031. 2

%I

%S 1,5,15,31,61,97,145,199,265,337,421,511,613,721,841,967,1105,1249,

%T 1405,1567,1741,1921,2113,2311,2521,2737,2965,3199,3445,3697,3961,

%U 4231,4513,4801,5101,5407,5725,6049,6385,6727,7081,7441,7813,8191,8581,8977,9385,9799,10225,10657,11101,11551

%N Partial sums of A298031.

%H Colin Barker, <a href="/A298032/b298032.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 (2,0,-2,1).

%F G.f.: -(2*x^6 - 8*x^4 - 3*x^3 - 5*x^2 - 3*x - 1) / ((1 - x)^2*(1 - x^2)).

%F From _Colin Barker_, Jan 25 2018: (Start)

%F a(n) = (9*n^2 - 6*n + 2) / 2 for n>2 and even.

%F a(n) = (9*n^2 - 6*n - 1) / 2 for n>2 and odd.

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

%F (End)

%o (PARI) Vec((1 + 3*x + 5*x^2 + 3*x^3 + 8*x^4 - 2*x^6) / ((1 - x)^3*(1 + x)) + O(x^50)) \\ _Colin Barker_, Jan 25 2018

%Y Cf. A298031.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Jan 21 2018

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Last modified September 25 22:18 EDT 2021. Contains 347664 sequences. (Running on oeis4.)