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

Author

Alejandro J. Becerra Jr., Aug 15 2018

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A092182.

Programs

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 *)

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

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)