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
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).
Crossrefs
Row n=3 of A213191.
Programs
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Maple
a:= n-> 4+2^n+3^n: seq(a(n), n=0..30);
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Mathematica
LinearRecurrence[{6,-11,6},{6,9,17},30] (* Harvey P. Dale, Jun 21 2022 *)
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)).