cp's OEIS Frontend

A225144 a(n) = Sum_{i=n..2*n} i^2*(-1)^i.

%I A225144 #21 Sep 08 2022 08:46:04
%S A225144 0,3,11,18,42,45,93,84,164,135,255,198,366,273,497,360,648,459,819,
%T A225144 570,1010,693,1221,828,1452,975,1703,1134,1974,1305,2265,1488,2576,
%U A225144 1683,2907,1890,3258,2109,3629,2340,4020,2583,4431,2838,4862,3105,5313,3384
%N A225144 a(n) = Sum_{i=n..2*n} i^2*(-1)^i.
%C A225144 3 and 11 are the only primes in the sequence.
%H A225144 Bruno Berselli, <a href="/A225144/b225144.txt">Table of n, a(n) for n = 0..1000</a>
%H A225144 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-3,0,1).
%F A225144 G.f.: x*(3+11*x+9*x^2+9*x^3)/(1-x^2)^3.
%F A225144 a(n) = 3*a(n-2)-3*a(n-4)+a(n-6).
%F A225144 a(n) = n*(4*n+(n-1)*(-1)^n+2)/2.
%F A225144 a(n) = A000217(2n) +(-1)^n*A000217(n-1) with A000217(-1)=0.
%F A225144 a(2n-1) = A094159(n) for n>0; a(2n) = A055437(n) for A055437(0)=0.
%e A225144 a(6) = 6^2-7^2+8^2-9^2+10^2-11^2+12^2 = 93.
%e A225144 a(7) = -7^2+8^2-9^2+10^2-11^2+12^2-13^2+14^2 = 84.
%t A225144 Table[Sum[i^2 (-1)^i, {i, n, 2 n}], {n, 0, 50}]
%o A225144 (Magma) [&+[i^2*(-1)^i: i in [n..2*n]]: n in [0..50]];
%Y A225144 Cf. A050409: sum(i^2, i=n..2n); A064455: sum(i*(-1)^i, i=n..2n); A065679: A000217(n)+(-1)^n*A000217(n-1); A089594: sum(i^2*(-1)^i, i=1..n).
%K A225144 nonn,easy
%O A225144 0,2
%A A225144 _Bruno Berselli_, Jun 06 2013