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A231306 Recurrence a(n) = a(n-2) + n^M for M=7, starting with a(0)=0, a(1)=1. 7
0, 1, 128, 2188, 16512, 80313, 296448, 903856, 2393600, 5686825, 12393600, 25173996, 48225408, 87922513, 153638912, 258781888, 422074368, 669120561, 1034294400, 1562992300, 2314294400, 3364080841, 4808652288, 6768906288, 9395123712, 12872421913, 17426933888 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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 (8,-27,48,-42,0,42,-48,27,-8,1).
FORMULA
a(n) = Sum_{k=0..floor(n/2)} (n-2k)^7.
From Colin Barker, Dec 22 2015: (Start)
a(n) = 1/96*(6*n^8+48*n^7+112*n^6-224*n^4+256*n^2+51*((-1)^n-1)).
G.f.: x*(1+120*x+1191*x^2+2416*x^3+1191*x^4+120*x^5+x^6) / ((1-x)^9*(1+x)).
(End)
EXAMPLE
a(5) = 5^7 + 3^7 + 1^7 = 80313.
MATHEMATICA
Table[SeriesCoefficient[x (1 + 120 x + 1191 x^2 + 2416 x^3 + 1191 x^4 + 120 x^5 + x^6)/((1 - x)^9 (1 + x)), {x, 0, n}], {n, 0, 26}] (* Michael De Vlieger, Dec 22 2015 *)
LinearRecurrence[{8, -27, 48, -42, 0, 42, -48, 27, -8, 1}, {0, 1, 128, 2188, 16512, 80313, 296448, 903856, 2393600, 5686825}, 30] (* Vincenzo Librandi, Dec 23 2015 *)
nxt[{n_, a_, b_}]:={n+1, b, a+(n+1)^7}; NestList[nxt, {1, 0, 1}, 30][[All, 2]] (* Harvey P. Dale, Jun 16 2022 *)
PROG
(PARI) nmax=100; a = vector(nmax); a[2]=1; for(i=3, #a, a[i]=a[i-2]+(i-1)^7); print(a);
(PARI) concat(0, Vec(x*(1+120*x+1191*x^2+2416*x^3+1191*x^4+120*x^5+x^6)/((1-x)^9*(1+x)) + O(x^50))) \\ 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), A231307 (M=8), A231308 (M=9), A231309 (M=10).
Sequence in context: A092759 A056574 A096961 * A236209 A283548 A297687
KEYWORD
nonn,easy
AUTHOR
Stanislav Sykora, Nov 07 2013
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)