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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
0, 1, 512, 19684, 262656, 1972809, 10340352, 42326416, 144558080, 429746905, 1144558080, 2787694596, 6304338432, 13392193969, 26965385216, 51835553344, 95684861952, 170423429841, 294044152320, 493111127620, 806044152320, 1287391174201, 2013313370112 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Stanislav Sykora, Table of n, a(n) for n = 0..9999

Index entries for linear recurrences with constant coefficients, signature (10,-44,110,-165,132,0,-132,165,-110,44,-10,1).

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)

EXAMPLE

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

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 *)

PROG

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

(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

CROSSREFS

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).

Sequence in context: A179665 A056586 A096962 * A254735 A254914 A186831

Adjacent sequences:  A231305 A231306 A231307 * A231309 A231310 A231311

KEYWORD

nonn,easy

AUTHOR

Stanislav Sykora, Nov 07 2013

EXTENSIONS

PARI code corrected by Colin Barker, Dec 22 2015

STATUS

approved

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Last modified June 23 18:19 EDT 2017. Contains 288668 sequences.