A302561 Partial sums of A092182.

1, 121, 1068, 4720, 14705, 36981, 80416, 157368, 284265, 482185, 777436, 1202136, 1794793, 2600885, 3673440, 5073616, 6871281, 9145593, 11985580, 15490720, 19771521, 24950101, 31160768, 38550600, 47280025, 57523401, 69469596, 83322568, 99301945

Offset

1,2

Comments

Geometrically, the partial sums of A092182 may be interpreted as 5-dimensional hexacosichoronal hyperpyramidal numbers. The hexacosichoron is a convex regular 4-D polytope with Schlaefli symbol {3,3,5}.

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} A092182(k).

From Colin Barker, Aug 15 2018: (Start)

G.f.: x*(1 + 115*x + 357*x^2 + 107*x^3) / (1 - x)^6.

a(n) = (n*(12 + n - 64*n^2 + 5*n^3 + 58*n^4)) / 12.

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

Accumulate[LinearRecurrence[{5, -10, 10, -5, 1}, {1, 120, 947, 3652, 9985}, 30]] (* or *) LinearRecurrence[ {6, -15, 20, -15, 6, -1}, {1, 121, 1068, 4720, 14705, 36981}, 30] (* Harvey P. Dale, May 04 2024 *)

Prog

(PARI) Vec(x*(1 + 115*x + 357*x^2 + 107*x^3) / (1 - x)^6 + O(x^40)) \\ Colin Barker, Aug 15 2018
(PARI) a(n) = (n*(12 + n - 64*n^2 + 5*n^3 + 58*n^4)) / 12 \\ Colin Barker, Aug 15 2018

Crossrefs

Cf. A092182.

Sequence in context: A211472 A223389 A243810 * A120353 A175983 A307858

Adjacent sequences: A302558 A302559 A302560 * A302562 A302563 A302564

Keyword

nonn,easy

Author

Alejandro J. Becerra Jr., Aug 15 2018

Status

approved