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A271638 The total sum of the cubes of all parts of all compositions of n. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..29.

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

Cf. A027992 (sum of squares).

Sequence in context: A353620 A277229 A163724 * A238916 A084857 A349948

Adjacent sequences:  A271635 A271636 A271637 * A271639 A271640 A271641

KEYWORD

nonn,easy

AUTHOR

R. J. Mathar, Apr 11 2016

STATUS

approved

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Last modified August 15 11:25 EDT 2022. Contains 356145 sequences. (Running on oeis4.)