A302562 Partial sums of A092181.

1, 25, 178, 722, 2147, 5243, 11172, 21540, 38469, 64669, 103510, 159094, 236327, 340991, 479816, 660552, 892041, 1184289, 1548538, 1997338, 2544619, 3205763, 3997676, 4938860, 6049485, 7351461, 8868510, 10626238, 12652207, 14976007, 17629328, 20646032

Offset: 1

Author

Alejandro J. Becerra Jr., Aug 15 2018

Keywords

• nonn
• easy

Comments

Geometrically, the partial sums of A092181 may be interpreted as 5-dimensional icositetrachoronal hyperpyramidal numbers. The icositetrachoron is a convex regular 4-D polytope with Schlaefli symbol {3,4,3}.

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A092181.

Programs

Mathematica

Table[n*(7 - 10*n^2 + 15*n^3 + 18*n^4)/30, {n, 40}] (* Wesley Ivan Hurt, Oct 30 2022 *)

PARI

Vec(x*(1 + 19*x + 43*x^2 + 9*x^3) / (1 - x)^6 + O(x^40)) \\ Colin Barker, Aug 15 2018

PARI

a(n) = (n*(7 - 10*n^2 + 15*n^3 + 18*n^4)) / 30 \\ Colin Barker, Aug 15 2018

Formula

a(n) = Sum_{k=1..n} A092181(k).

From Colin Barker, Aug 15 2018: (Start)

G.f.: x*(1 + 19*x + 43*x^2 + 9*x^3) / (1 - x)^6.

a(n) = n*(7 - 10*n^2 + 15*n^3 + 18*n^4) / 30.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)