A390140 Centered truncated cube numbers: a(n) = (46*n^3 - 69*n^2 + 29*n - 3)/3.

1, 49, 235, 651, 1389, 2541, 4199, 6455, 9401, 13129, 17731, 23299, 29925, 37701, 46719, 57071, 68849, 82145, 97051, 113659, 132061, 152349, 174615, 198951, 225449, 254201, 285299, 318835, 354901, 393589, 434991, 479199, 526305, 576401, 629579, 685931, 745549, 808525

Offset

1,2

References

Elena Deza and Michel Marie Deza, Figurate numbers, World Scientific Publishing (2012), pages 136-137.

Links

Table of n, a(n) for n=1..38.

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

Formula

a(n) = (2*n - 1)*(23*n^2 - 23*n + 3)/3.

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

G.f.: x*(1 + 45*x + 45*x^2 + x^3)/(1 - x)^4.

E.g.f.: 1 + exp(x)*(46*x^3/3 + 23*x^2 + 2*x - 1).

Mathematica

a[n_]:=(46n^3-69n^2+29n-3)/3; Array[a, 38]

Crossrefs

Partial sums of A005911.

Sequence in context: A137880 A264538 A266799 * A211741 A211761 A373707

Adjacent sequences: A390137 A390138 A390139 * A390141 A390142 A390143

Keyword

nonn,easy

Author

Stefano Spezia, Oct 26 2025

Status

approved