A231308 Recurrence a(n) = a(n-2) + n^M for M=9, starting with a(0)=0, a(1)=1.
0, 1, 512, 19684, 262656, 1972809, 10340352, 42326416, 144558080, 429746905, 1144558080, 2787694596, 6304338432, 13392193969, 26965385216, 51835553344, 95684861952, 170423429841, 294044152320, 493111127620, 806044152320, 1287391174201, 2013313370112
Offset: 0
Examples
a(5) = 5^9 + 3^9 + 1^9 = 1972809.
Links
- Stanislav Sykora, Table of n, a(n) for n = 0..9999
- Stanislav Sýkora, Magnetic Resonance on OEIS, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019.
- Index entries for linear recurrences with constant coefficients, signature (10,-44,110,-165,132,0,-132,165,-110,44,-10,1).
Crossrefs
Programs
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Mathematica
RecurrenceTable[{a[0]==0,a[1]==1,a[n]==a[n-2]+n^9},a,{n,30}] (* or *) 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 *) -
PARI
nmax=100; a = vector(nmax); a[2]=1; for(i=3, #a, a[i]=a[i-2]+(i-1)^9); print(a);
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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
Formula
a(n) = Sum{k=0..floor(n/2)}(n-2k)^9.
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
From Colin Barker, Dec 22 2015: (Start)
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)).
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)
Extensions
PARI code corrected by Colin Barker, Dec 22 2015