A229354 Total sum of n-th powers of parts in all partitions of 3.

6, 9, 17, 39, 101, 279, 797, 2319, 6821, 20199, 60077, 179199, 535541, 1602519, 4799357, 14381679, 43112261, 129271239, 387682637, 1162785759, 3487832981, 10462450359, 31385253917, 94151567439, 282446313701, 847322163879, 2541932937197, 7625731702719

Offset

0,1

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

Formula

a(n) = Sum_{k=1..3} A066633(3,k) * k^n.

a(n) = 4 + 2^n + 3^n.

G.f.: -(29*x^2-27*x+6)/((x-1)*(2*x-1)*(3*x-1)).

Maple

a:= n-> 4+2^n+3^n:
seq(a(n), n=0..30);

Mathematica

LinearRecurrence[{6, -11, 6}, {6, 9, 17}, 30] (* Harvey P. Dale, Jun 21 2022 *)

Crossrefs

Row n=3 of A213191.

Sequence in context: A316067 A316068 A327796 * A316069 A351851 A301720

Adjacent sequences: A229351 A229352 A229353 * A229355 A229356 A229357

Keyword

nonn,easy

Author

Alois P. Heinz, Sep 20 2013

Status

approved