A271638 The total sum of the cubes of all parts of all compositions of n.

1, 10, 48, 170, 512, 1398, 3580, 8770, 20808, 48206, 109652, 245850, 544864, 1196134, 2605164, 5636210, 12124280, 25952382, 55312516, 117440650, 248512656, 524288150, 1103102108, 2315255970, 4848615592, 10133438638, 21139292340, 44023414970, 91536490688

Offset: 1

Author

R. J. Mathar, Apr 11 2016

Keywords

• nonn
• easy

Examples

			The two compositions of n=2 are 2 and 1+1. The total sum of the cubes is a(2) = 2^3+1^3+1^3 = 10.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-13,12,-4).

Crossrefs

Cf. A027992 (sum of squares).

Programs

Mathematica

Table[(13 n - 36) 2^(n - 1) + 6 n + 18, {n, 29}] (* or *)
Rest@ CoefficientList[Series[x (1 + 4 x + x^2)/((1 - 2 x) (1 - x))^2, {x, 0, 29}], x] (* Michael De Vlieger, Apr 11 2016 *)

PARI

x='x+O('x^99); Vec(x*(1+4*x+x^2)/((2*x-1)*(1-x))^2) \\ Altug Alkan, Apr 11 2016

Python

for n in range(1,50):print((13*n-36)*2**(n-1)+6*n+18) # Soumil Mandal, Apr 11 2016

Formula

G.f.: x*(1 + 4*x + x^2)/((1 - 2*x)*(1 - x))^2.

a(n) = (13*n - 36)*2^(n - 1) + 6*n + 18.