cp's OEIS Frontend

A231309 Recurrence a(n) = a(n-2) + n^M for M=10, starting with a(0)=0, a(1)=1.

%I A231309 #25 Nov 21 2019 00:10:50
%S A231309 0,1,1024,59050,1049600,9824675,61515776,292299924,1135257600,
%T A231309 3779084325,11135257600,29716508926,73052621824,167575000775,
%U A231309 362307276800,744225391400,1461818904576,2760219291849,5032286131200,8891285549650,15272286131200
%N A231309 Recurrence a(n) = a(n-2) + n^M for M=10, starting with a(0)=0, a(1)=1.
%H A231309 Stanislav Sykora, <a href="/A231309/b231309.txt">Table of n, a(n) for n = 0..9999</a>
%H A231309 Stanislav Sýkora, <a href="http://www.ebyte.it/stan/blog12to14.html#14Dec31">Magnetic Resonance on OEIS</a>, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019.
%H A231309 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
%F A231309 a(n) = Sum_{k=0..floor(n\2)} (n-2*k)^10.
%F A231309 From _Colin Barker_, Dec 22 2015: (Start)
%F A231309 a(n) = (1/66)*n*(3*n^10 + 33*n^9 + 110*n^8 - 528*n^6 + 2112*n^4 - 4224*n^2 + 2560).
%F A231309 G.f.: x*(1 + 1012*x + 46828*x^2 + 408364*x^3 + 901990*x^4 + 408364*x^5 + 46828*x^6 + 1012*x^7 + x^8) / (1-x)^12.
%F A231309 (End)
%e A231309 a(5) = 5^10 + 3^10 + 1^10 = 9824675.
%t A231309 CoefficientList[Series[x (1 + 1012 x + 46828 x^2 + 408364 x^3 + 901990 x^4 + 408364 x^5 + 46828 x^6 + 1012 x^7 + x^8)/(1 - x)^12, {x, 0, 20}], x] (* _Michael De Vlieger_, Nov 20 2019 *)
%o A231309 (PARI) nmax=100; a=vector(nmax); a[2]=1; for(i=3, #a, a[i]=a[i-2]+(i-1)^10); print(a);
%o A231309 (PARI) concat(0, Vec(x*(1 +1012*x +46828*x^2 +408364*x^3 +901990*x^4 +408364*x^5 +46828*x^6 +1012*x^7 +x^8) / (1 -x)^12 + O(x^40))) \\ _Colin Barker_, Dec 22 2015
%Y A231309 Cf. A001477 (M=1), A000292 (M=2), A105636 (M=3), A231303 (M=4), A231304 (M=5), A231305 (M=6), A231306 (M=7), A231307 (M=8), A231308 (M=9).
%K A231309 nonn,easy
%O A231309 0,3
%A A231309 _Stanislav Sykora_, Nov 07 2013