A393148 Partial sums of truncated triangular pyramid numbers.

1, 8, 27, 65, 130, 231, 378, 582, 855, 1210, 1661, 2223, 2912, 3745, 4740, 5916, 7293, 8892, 10735, 12845, 15246, 17963, 21022, 24450, 28275, 32526, 37233, 42427, 48140, 54405, 61256, 68728, 76857, 85680, 95235, 105561, 116698, 128687, 141570, 155390, 170191, 186018, 202917, 220935

Offset

4,2

Comments

Binomial transform of [1, 7, 12, 7, 1, 0, 0, 0, ...] (with offset 0).

Links

Table of n, a(n) for n=4..47.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = (1/24)*(n-3)*(n-2)*(n^2 + 11*n - 48).

a(n) = Sum_{k=4..n} (k-3)*(k^2+6*k-34)/6.

G.f.: x^4*(1+3*x-3*x^2)/(1-x)^5.

E.g.f.: 3*(4 + x) - exp(x)*(12 - 9*x + 3*x^2 - x^3/2 - x^4/24). - Stefano Spezia, Mar 15 2026

Mathematica

a[n_]:=(1/24)*(n-3)*(n-2)*(n^2 + 11*n - 48); Array[a, 44, 4] (* Stefano Spezia, Mar 15 2026 *)

Crossrefs

Cf. A051937.

Sequence in context: A030293 A030479 A061096 * A084825 A270806 A372227

Adjacent sequences: A393145 A393146 A393147 * A393149 A393150 A393151

Keyword

nonn,easy

Author

Enrique Navarrete, Mar 10 2026

Status

approved