OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
a(n) ~ c * d^n, where d = 1.480632733359847628849916564959539381483927975663120268887..., c = 0.6193575859000249187293498067457554927448225891538342... . - Vaclav Kotesovec, Sep 02 2014
EXAMPLE
a(5) = 5: [5], [3,1,1], [1,3,1], [1,1,3], [1,1,1,1,1].
a(6) = 10: [6], [4,2], [3,3], [3,1,1,1], [2,4], [2,2,2], [1,3,1,1], [1,1,3,1], [1,1,1,3], [1,1,1,1,1,1].
MAPLE
b:= proc(n, i) option remember; `if`(n<1 or i<1, 0,
`if`(n=i, 1, add(b(n-i, i+j), j=[-2, 0, 2])))
end:
a:= n-> `if`(n=0, 1, add(b(n, j), j=1..n)):
seq(a(n), n=0..60);
MATHEMATICA
b[n_, i_] := b[n, i] = If[n < 1 || i < 1, 0, If[n == i, 1, Sum[b[n-i, i+j], {j, {-2, 0, 2}}]]]; a[n_] := If[n == 0, 1, Sum[b[n, j], {j, 1, n}]]; Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Nov 06 2014, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 08 2012
STATUS
approved