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

1,2

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).

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)

Mathematica

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

Prog

(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

Crossrefs

Cf. A092181.

Sequence in context: A200671 A042212 A258319 * A264259 A209858 A209851

Adjacent sequences: A302559 A302560 A302561 * A302563 A302564 A302565

Keyword

nonn,easy

Author

Alejandro J. Becerra Jr., Aug 15 2018

Status

approved