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

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..40.

Formula

a(n)=(2*n-1)*(n^2-n+4)/2 = (2*n-1)*A089071(n+1) = 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. [From R. J. Mathar, Mar 31 2010]

Mathematica

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

Crossrefs

Cf. A027575, A173960, A173961, A173962

Sequence in context: A053194 A346069 A005582 * A116454 A295143 A124633

Adjacent sequences: A173962 A173963 A173964 * A173966 A173967 A173968

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Mar 03 2010

Status

approved