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A231304 Recurrence a(n) = a(n-2) + n^M for M=5, starting with a(0)=0, a(1)=1. 7

%I

%S 0,1,32,244,1056,3369,8832,20176,41600,79225,141600,240276,390432,

%T 611569,928256,1370944,1976832,2790801,3866400,5266900,7066400,

%U 9351001,12220032,15787344,20182656,25552969,32064032,39901876,49274400,60413025,73574400,89042176

%N Recurrence a(n) = a(n-2) + n^M for M=5, starting with a(0)=0, a(1)=1.

%C See A231303.

%H Stanislav Sykora, <a href="/A231304/b231304.txt">Table of n, a(n) for n = 0..9999</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (6,-14,14,0,-14,14,-6,1).

%F a(n) = Sum_{k=0..floor(n/2)} (n-2k)^5.

%F a(0)=0, a(1)=1, a(2)=32, a(3)=244, a(4)=1056, a(5)=3369, a(6)=8832, a(7)=20176, a(n) = 6*a(n-1)-14*a(n-2)+14*a(n-3)-14*a(n-5)+ 14*a(n-6)- 6*a(n-7)+ a(n-8). - _Harvey P. Dale_, Jul 22 2014

%F From _Colin Barker_, Dec 22 2015: (Start)

%F a(n) = 1/24*(2*n^6+12*n^5+20*n^4-16*n^2-3*(-1)^n+3).

%F G.f.: x*(1+26*x+66*x^2+26*x^3+x^4) / ((1-x)^7*(1+x)).

%F (End)

%e a(4) = 4^5 + 2^5 = 1056; a(5) = 5^5 + 3^5 + 1^5 = 3369.

%t RecurrenceTable[{a[0]==0,a[1]==1,a[n]==a[n-2]+n^5},a,{n,30}] (* or *) LinearRecurrence[{6,-14,14,0,-14,14,-6,1},{0,1,32,244,1056,3369,8832,20176},40] (* _Harvey P. Dale_, Jul 22 2014 *)

%o (PARI) nmax=100; a = vector(nmax); a[2]=1; for(i=3, #a, a[i]=a[i-2]+(i-1)^5); print(a);

%o (PARI) concat(0, Vec(x*(1+26*x+66*x^2+26*x^3+x^4)/((1-x)^7*(1+x)) + O(x^50))) \\ _Colin Barker_, Dec 22 2015

%Y Cf. A001477 (M=1), A000292 (M=2), A105636 (M=3), A231303 (M=4), A231305 (M=6), A231306 (M=7), A231307 (M=8), A231308 (M=9), A231309 (M=10).

%K nonn,easy

%O 0,3

%A _Stanislav Sykora_, Nov 07 2013

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Last modified January 21 11:54 EST 2019. Contains 319356 sequences. (Running on oeis4.)