A302559 Partial sums of A092183.

1, 601, 5584, 25052, 78557, 198233, 431928, 846336, 1530129, 2597089, 4189240, 6479980, 9677213, 14026481, 19814096, 27370272, 37072257, 49347465, 64676608, 83596828, 106704829, 134660009, 168187592, 208081760, 255208785, 310510161

Offset: 1

Author

Alejandro J. Becerra Jr., Aug 15 2018

Keywords

• nonn
• easy

Comments

Geometrically, the partial sums of A092183 may be interpreted as 5-dimensional hecatonicosachoronal hyperpyramidal numbers. The hecatonicosachoron is a convex regular 4-D polytope with Schlaefli symbol {5,3,3}.

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. A092183.

Programs

PARI

Vec(x*(1 + 595*x + 1993*x^2 + 543*x^3) / (1 - x)^6 + O(x^40)) \\ Colin Barker, Aug 15 2018

PARI

a(n) = (n*(584 - 105*n - 2120*n^2 + 135*n^3 + 1566*n^4)) / 60 \\ Colin Barker, Aug 15 2018

Formula

a(n) = Sum_{k=1..n} A092183(k).

From Colin Barker, Aug 15 2018: (Start)

G.f.: x*(1 + 595*x + 1993*x^2 + 543*x^3) / (1 - x)^6.

a(n) = n*(584 - 105*n - 2120*n^2 + 135*n^3 + 1566*n^4)/60.

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)