cp's OEIS Frontend

A231307 Recurrence a(n) = a(n-2) + n^M for M=8, starting with a(0)=0, a(1)=1.

%I A231307 #28 Sep 08 2022 08:46:06
%S A231307 0,1,256,6562,65792,397187,1745408,6161988,18522624,49208709,
%T A231307 118522624,263567590,548504320,1079298311,2024293376,3642188936,
%U A231307 6319260672,10617946377,17339221248,27601509418,42939221248,65424368779,97815094784,143735354060
%N A231307 Recurrence a(n) = a(n-2) + n^M for M=8, starting with a(0)=0, a(1)=1.
%H A231307 Stanislav Sykora, <a href="/A231307/b231307.txt">Table of n, a(n) for n = 0..9999</a>
%H A231307 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 A231307 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F A231307 a(n) = Sum_{k=0..floor(n/2)} (n-2k)^8.
%F A231307 a(n) = 1/90*n*(n+1)*(n+2)*(5*n^6+30*n^5+20*n^4-120*n^3-16*n^2+288*n-192). - _Vaclav Kotesovec_, Feb 14 2014
%F A231307 G.f.: x*(1+246*x+4047*x^2+11572*x^3+4047*x^4+246*x^5+x^6) / (1-x)^10.
%e A231307 a(5) = 5^8 + 3^8 + 1^8 = 397187.
%t A231307 Table[1/90*n*(n+1)*(n+2)*(5*n^6+30*n^5+20*n^4-120*n^3-16*n^2+288*n-192),{n,0,20}] (* _Vaclav Kotesovec_, Feb 14 2014 *)
%o A231307 (PARI) nmax=100; a = vector(nmax); a[2]=1; for(i=3, #a, a[i]=a[i-2]+(i-1)^8); print(a);
%o A231307 (PARI) concat(0, Vec(x*(1+246*x+4047*x^2+11572*x^3+4047*x^4+246*x^5+x^6)/(1-x)^10 + O(x^50))) \\ _Colin Barker_, Dec 22 2015
%o A231307 (Magma) [1/90*n*(n+1)*(n+2)*(5*n^6+30*n^5+20*n^4-120*n^3-16*n^2+288*n-192): n in [0..30]]; // _Vincenzo Librandi_, Dec 23 2015
%Y A231307 Cf. A001477 (M=1), A000292 (M=2), A105636 (M=3), A231303 (M=4), A231304 (M=5), A231305 (M=6), A231306 (M=7), A231308 (M=9), A231309 (M=10).
%K A231307 nonn,easy
%O A231307 0,3
%A A231307 _Stanislav Sykora_, Nov 07 2013