A102713 Total sum of odd parts in all compositions of n.
1, 2, 8, 18, 48, 110, 260, 586, 1320, 2918, 6412, 13954, 30192, 64926, 138964, 296122, 628664, 1330134, 2805916, 5903090, 12388736, 25942542, 54215268, 113090858, 235502408, 489646150, 1016575020, 2107715426, 4364561680, 9027384958, 18651293172, 38495632794
Offset: 1
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (2,3,-4,-4).
Programs
-
PARI
a(n)={((15*n+4)*2^(n-1) - 2*(3*n+1)*(-1)^n)/27} \\ Andrew Howroyd, Jan 08 2020 -
PARI
Vec(x*(1 + x^2) / ((1 + x)^2*(1 - 2*x)^2) + O(x^35)) \\ Colin Barker, Jan 08 2020
Formula
a(n) = ((15*n+4)*2^(n-1)-2*(3*n+1)*(-1)^n)/27.
From Colin Barker, Jan 08 2020: (Start)
G.f.: x*(1 + x^2) / ((1 + x)^2*(1 - 2*x)^2).
a(n) = 2*a(n-1) + 3*a(n-2) - 4*a(n-3) - 4*a(n-4) for n>4.
(End)
Extensions
Terms a(26) and beyond from Andrew Howroyd, Jan 08 2020