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A231308 Recurrence a(n) = a(n-2) + n^M for M=9, starting with a(0)=0, a(1)=1. 7

%I

%S 0,1,512,19684,262656,1972809,10340352,42326416,144558080,429746905,

%T 1144558080,2787694596,6304338432,13392193969,26965385216,51835553344,

%U 95684861952,170423429841,294044152320,493111127620,806044152320,1287391174201,2013313370112

%N Recurrence a(n) = a(n-2) + n^M for M=9, starting with a(0)=0, a(1)=1.

%H Stanislav Sykora, <a href="/A231308/b231308.txt">Table of n, a(n) for n = 0..9999</a>

%H 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 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (10,-44,110,-165,132,0,-132,165,-110,44,-10,1).

%F a(n) = Sum{k=0..floor(n/2)}(n-2k)^9.

%F a(0)=0, a(1)=1, a(2)=512, a(3)=19684, a(4)=262656, a(5)=1972809, a(6)=10340352, a(7)=42326416, a(8)=144558080, a(9)=429746905, a(10)=1144558080, a(11)=2787694596, a(n) = 10*a(n-1) - 44*a(n-2) + 110*a(n-3) - 165*a(n-4) + 132*a(n-5) - 132*a(n-7) + 165*a(n-8) - 110*a(n-9) + 44*a(n-10) - 10*a(n-11) + a(n-12). - _Harvey P. Dale_, Apr 29 2014

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

%F a(n) = (1/40)*(2*n^10 + 20*n^9 + 60*n^8 - 224*n^6 + 640*n^4 - 768*n^2 - 155*((-1)^n -1)).

%F G.f.: x*(1 + 502*x + 14608*x^2 + 88234*x^3 + 156190*x^4 + 88234*x^5 + 14608*x^6 + 502*x^7 + x^8) / ((1-x)^11*(1+x)). (End)

%e a(5) = 5^9 + 3^9 + 1^9 = 1972809.

%t RecurrenceTable[{a[0]==0,a[1]==1,a[n]==a[n-2]+n^9},a,{n,30}] (* or *)

%t LinearRecurrence[{10,-44,110,-165,132,0,-132,165,-110,44,-10,1},{0,1,512,19684,262656,1972809,10340352,42326416,144558080,429746905,1144558080,2787694596},30] (* _Harvey P. Dale_, Apr 29 2014 *)

%o (PARI) nmax=100; a = vector(nmax); a[2]=1; for(i=3, #a, a[i]=a[i-2]+(i-1)^9); print(a);

%o (PARI) concat(0, Vec(x*(1 +502*x +14608*x^2 +88234*x^3 +156190*x^4 +88234*x^5 +14608*x^6 +502*x^7 +x^8) / ((1 -x)^11*(1 +x)) + O(x^40))) \\ _Colin Barker_, Dec 22 2015

%Y 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), A231309 (M=10).

%K nonn,easy,changed

%O 0,3

%A _Stanislav Sykora_, Nov 07 2013

%E PARI code corrected by _Colin Barker_, Dec 22 2015

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Last modified November 22 16:13 EST 2019. Contains 329396 sequences. (Running on oeis4.)