OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
a(n) ~ c * d^n, where d = 1.517398641547133636808941933115508174163721854365273284016518..., c = 0.733002948674062952076493110095119568735789170592785923762247... . - Vaclav Kotesovec, Sep 02 2014
EXAMPLE
a(4) = 4: [4], [3,1], [1,3], [1,2,1].
a(5) = 5: [5], [3,2], [2,3], [2,1,2], [1,3,1].
a(6) = 11: [6], [4,2], [3,2,1], [3,1,2], [2,4], [2,3,1], [2,1,3], [2,1,2,1], [1,3,2], [1,2,3], [1,2,1,2].
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, -1, 1, 2])))
end:
a:= n-> `if`(n=0, 1, add(b(n, j), j=1..n)):
seq(a(n), n=0..70);
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, -1, 1, 2}}]]]; a[n_] := If[n == 0, 1, Sum[b[n, j], {j, 1, n}]]; Table[a[n], {n, 0, 70}] (* Jean-François Alcover, Nov 06 2014, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 08 2012
STATUS
approved