A173965 Averages of four consecutive cubes.

2, 9, 25, 56, 108, 187, 299, 450, 646, 893, 1197, 1564, 2000, 2511, 3103, 3782, 4554, 5425, 6401, 7488, 8692, 10019, 11475, 13066, 14798, 16677, 18709, 20900, 23256, 25783, 28487, 31374, 34450, 37721, 41193, 44872, 48764, 52875, 57211, 61778, 66582, 71629, 76925

Offset

1,1

Links

Table of n, a(n) for n=1..43.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

From R. J. Mathar, Mar 31 2010: (Start)

a(n) = (2*n-1)*(n^2-n+4)/2 = (2*n-1)*A089071(n+1).

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

G.f.: x*(1+x)*(2*x^2-x+2)/(x-1)^4. (End)

E.g.f.: 2 + exp(x)*(-4 + 8*x + 3*x^2 + 2*x^3)/2. - Elmo R. Oliveira, Aug 23 2025

Example

(0^3+1^3+2^3+3^3)/4 = 9, ...

Mathematica

f[n_]:=(n^3+(n+1)^3+(n+2)^3+(n+3)^3)/4; Table[f[n], {n, -1, 5!}]

Crossrefs

Cf. A027575, A089071, A173960, A173961, A173962.

Sequence in context: A388976 A346069 A005582 * A116454 A295143 A124633

Adjacent sequences: A173962 A173963 A173964 * A173966 A173967 A173968

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Mar 03 2010

Extensions

More terms from Elmo R. Oliveira, Aug 23 2025

Status

approved