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
Examples
(0^3+1^3+2^3+3^3)/4 = 9, ...
Links
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Mathematica
f[n_]:=(n^3+(n+1)^3+(n+2)^3+(n+3)^3)/4;Table[f[n],{n,-1,5!}]
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
Extensions
More terms from Elmo R. Oliveira, Aug 23 2025