OFFSET
1,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (6,-13,12,-4).
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.
EXAMPLE
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.
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Apr 11 2016
STATUS
approved