A214255 Number of compositions of n where differences between neighboring parts are in {-2,...,2}.

1, 1, 2, 4, 8, 14, 27, 49, 92, 170, 317, 587, 1097, 2038, 3798, 7072, 13176, 24538, 45720, 85166, 158670, 295596, 550708, 1025974, 1911445, 3561079, 6634457, 12360279, 23027789, 42901825, 79928175, 148909982, 277426505, 516858952, 962933307, 1793991419

Offset

0,3

Links

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

Formula

a(n) ~ c * d^n, where d = 1.8630486786572002290749607226537419966705160765891889162715127426..., c = 0.6251341184281574379681933375704862852528326365321195333127800734... . - Vaclav Kotesovec, Sep 02 2014

Example

a(3) = 4: [3], [2,1], [1,2], [1,1,1].
a(4) = 8: [4], [3,1], [2,2], [2,1,1], [1,3], [1,2,1], [1,1,2], [1,1,1,1].
a(5) = 14: [5], [3,2], [3,1,1], [2,3], [2,2,1], [2,1,2], [2,1,1,1], [1,3,1], [1,2,2], [1,2,1,1], [1,1,3], [1,1,2,1], [1,1,1,2], [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..2)))
    end:
a:= n-> `if`(n=0, 1, add(b(n, j), j=1..n)):
seq(a(n), n=0..50);

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, 2}]]]; a[n_] := If[n == 0, 1, Sum[b[n, j], {j, 1, n}]]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Nov 06 2014, after Alois P. Heinz *)

Crossrefs

Column k=2 of A214248.

Sequence in context: A048238 A048140 A179817 * A065616 A164147 A321402

Adjacent sequences: A214252 A214253 A214254 * A214256 A214257 A214258

Keyword

nonn

Author

Alois P. Heinz, Jul 08 2012

Status

approved