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

1,2

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).

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)

Prog

(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

Crossrefs

Cf. A092183.

Sequence in context: A255024 A362323 A283923 * A232073 A278206 A094231

Adjacent sequences: A302556 A302557 A302558 * A302560 A302561 A302562

Keyword

nonn,easy

Author

Alejandro J. Becerra Jr., Aug 15 2018

Status

approved