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A231306 Recurrence a(n) = a(n-2) + n^M for M=7, starting with a(0)=0, a(1)=1.

%I A231306 #30 Jun 16 2022 16:16:31
%S A231306 0,1,128,2188,16512,80313,296448,903856,2393600,5686825,12393600,
%T A231306 25173996,48225408,87922513,153638912,258781888,422074368,669120561,
%U A231306 1034294400,1562992300,2314294400,3364080841,4808652288,6768906288,9395123712,12872421913,17426933888
%N A231306 Recurrence a(n) = a(n-2) + n^M for M=7, starting with a(0)=0, a(1)=1.
%H A231306 Stanislav Sykora, <a href="/A231306/b231306.txt">Table of n, a(n) for n = 0..9999</a>
%H A231306 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 A231306 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (8,-27,48,-42,0,42,-48,27,-8,1).
%F A231306 a(n) = Sum_{k=0..floor(n/2)} (n-2k)^7.
%F A231306 From _Colin Barker_, Dec 22 2015: (Start)
%F A231306 a(n) = 1/96*(6*n^8+48*n^7+112*n^6-224*n^4+256*n^2+51*((-1)^n-1)).
%F A231306 G.f.: x*(1+120*x+1191*x^2+2416*x^3+1191*x^4+120*x^5+x^6) / ((1-x)^9*(1+x)).
%F A231306 (End)
%e A231306 a(5) = 5^7 + 3^7 + 1^7 = 80313.
%t A231306 Table[SeriesCoefficient[x (1 + 120 x + 1191 x^2 + 2416 x^3 + 1191 x^4 + 120 x^5 + x^6)/((1 - x)^9 (1 + x)), {x, 0, n}], {n, 0, 26}] (* _Michael De Vlieger_, Dec 22 2015 *)
%t A231306 LinearRecurrence[{8, -27, 48, -42, 0, 42, -48, 27, -8, 1}, {0, 1, 128, 2188, 16512, 80313, 296448, 903856, 2393600, 5686825}, 30] (* _Vincenzo Librandi_, Dec 23 2015 *)
%t A231306 nxt[{n_,a_,b_}]:={n+1,b,a+(n+1)^7}; NestList[nxt,{1,0,1},30][[All,2]] (* _Harvey P. Dale_, Jun 16 2022 *)
%o A231306 (PARI) nmax=100; a = vector(nmax); a[2]=1; for(i=3, #a, a[i]=a[i-2]+(i-1)^7); print(a);
%o A231306 (PARI) concat(0, Vec(x*(1+120*x+1191*x^2+2416*x^3+1191*x^4+120*x^5+x^6)/((1-x)^9*(1+x)) + O(x^50))) \\ _Colin Barker_, Dec 22 2015
%Y A231306 Cf. A001477 (M=1), A000292 (M=2), A105636 (M=3), A231303 (M=4), A231304 (M=5), A231305 (M=6), A231307 (M=8), A231308 (M=9), A231309 (M=10).
%K A231306 nonn,easy
%O A231306 0,3
%A A231306 _Stanislav Sykora_, Nov 07 2013