A302560 Partial sums of icosahedral numbers (A006564).

1, 13, 61, 185, 440, 896, 1638, 2766, 4395, 6655, 9691, 13663, 18746, 25130, 33020, 42636, 54213, 68001, 84265, 103285, 125356, 150788, 179906, 213050, 250575, 292851, 340263, 393211, 452110, 517390, 589496, 668888, 756041, 851445, 955605, 1069041, 1192288, 1325896

Offset: 1

Author

Alejandro J. Becerra Jr., Aug 15 2018

Keywords

• nonn
• easy

Comments

Geometrically, the partial sums of A006564 may be interpreted as 4-dimensional icosahedral hyperpyramidal numbers.

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A006564.

Programs

PARI

Vec(x*(1 + 8*x + 6*x^2) / (1 - x)^5 + O(x^40)) \\ Colin Barker, Aug 15 2018

PARI

a(n) = (n*(2 - 3*n + 10*n^2 + 15*n^3)) / 24 \\ Colin Barker, Aug 15 2018

Formula

a(n) = Sum_{k=1..n} A006564(k).

From Colin Barker, Aug 15 2018: (Start)

G.f.: x*(1 + 8*x + 6*x^2) / (1 - x)^5.

a(n) = n*(2 - 3*n + 10*n^2 + 15*n^3)/24.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)