A231305 Recurrence a(n) = a(n-2) + n^M for M=6, starting with a(0)=0, a(1)=1.

0, 1, 64, 730, 4160, 16355, 50816, 134004, 312960, 665445, 1312960, 2437006, 4298944, 7263815, 11828480, 18654440, 28605696, 42792009, 62617920, 89837890, 126617920, 175604011, 239997824, 323639900, 431100800, 567780525, 740016576, 955201014, 1221906880

Offset: 0

Author

Stanislav Sykora, Nov 07 2013

Keywords

• nonn
• easy
• changed

Examples

			a(5) = 5^6 + 3^6 + 1^6 = 16355.
		

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 (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Cf. A001477 (M=1), A000292 (M=2), A105636 (M=3), A231303 (M=4), A231304 (M=5), A231306 (M=7), A231307 (M=8), A231308 (M=9), A231309 (M=10).

Programs

Maple

map(op,ListTools:-PartialSums([seq([(2*i)^6,(2*i+1)^6],i=0..50)])); # Robert Israel, Dec 22 2015

Mathematica

Table[SeriesCoefficient[x (1 + 56 x + 246 x^2 + 56 x^3 + x^4)/(1 - x)^8, {x, 0, n}], {n, 0, 28}] (* Michael De Vlieger, Dec 22 2015 *)
LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{0,1,64,730,4160,16355,50816,134004},30] (* Harvey P. Dale, Aug 23 2025 *)

PARI

nmax=100; a = vector(nmax); a[2]=1; for(i=3, #a, a[i]=a[i-2]+(i-1)^6); print(a);

PARI

concat(0, Vec(x*(1+56*x+246*x^2+56*x^3+x^4)/(1-x)^8 + O(x^50))) \\ Colin Barker, Dec 22 2015

Formula

a(n) = Sum_{k=0..floor(n/2)}(n-2k)^6.

From Colin Barker, Dec 22 2015: (Start)

a(n) = 1/42*n*(3*n^6+21*n^5+42*n^4-56*n^2+32).

G.f.: x*(1+56*x+246*x^2+56*x^3+x^4) / (1-x)^8.

(End)