A214256 Number of compositions of n where differences between neighboring parts are in {-2,-1,1,2}.

1, 1, 1, 3, 4, 5, 11, 14, 18, 36, 49, 66, 118, 169, 238, 401, 586, 846, 1371, 2042, 2998, 4731, 7114, 10566, 16419, 24809, 37118, 57139, 86558, 130151, 199193, 302109, 455737, 695084, 1054761, 1594484, 2426813, 3683310, 5575665, 8475607, 12864385, 19490762

Offset: 0

Author

Alois P. Heinz, Jul 08 2012

Keywords

• nonn

Examples

			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].
		

Links

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

Crossrefs

Column k=2 of A214249.

Programs

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 *)

Formula

a(n) ~ c * d^n, where d = 1.517398641547133636808941933115508174163721854365273284016518..., c = 0.733002948674062952076493110095119568735789170592785923762247... . - Vaclav Kotesovec, Sep 02 2014