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

0, 1, 32, 244, 1056, 3369, 8832, 20176, 41600, 79225, 141600, 240276, 390432, 611569, 928256, 1370944, 1976832, 2790801, 3866400, 5266900, 7066400, 9351001, 12220032, 15787344, 20182656, 25552969, 32064032, 39901876, 49274400, 60413025, 73574400, 89042176

Offset

0,3

Comments

See A231303.

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 (6,-14,14,0,-14,14,-6,1).

Formula

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

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

From Colin Barker, Dec 22 2015: (Start)

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

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

(End)

Example

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

Mathematica

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 *)

Prog

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

Crossrefs

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).

Sequence in context: A056572 A226098 A096960 * A269079 A134846 A066392

Adjacent sequences: A231301 A231302 A231303 * A231305 A231306 A231307

Keyword

nonn,easy

Author

Stanislav Sykora, Nov 07 2013

Status

approved