cp's OEIS Frontend

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

%I A214255 #15 Nov 16 2014 15:09:21
%S A214255 1,1,2,4,8,14,27,49,92,170,317,587,1097,2038,3798,7072,13176,24538,
%T A214255 45720,85166,158670,295596,550708,1025974,1911445,3561079,6634457,
%U A214255 12360279,23027789,42901825,79928175,148909982,277426505,516858952,962933307,1793991419
%N A214255 Number of compositions of n where differences between neighboring parts are in {-2,...,2}.
%H A214255 Alois P. Heinz, <a href="/A214255/b214255.txt">Table of n, a(n) for n = 0..1000</a>
%F A214255 a(n) ~ c * d^n, where d = 1.8630486786572002290749607226537419966705160765891889162715127426..., c = 0.6251341184281574379681933375704862852528326365321195333127800734... . - _Vaclav Kotesovec_, Sep 02 2014
%e A214255 a(3) = 4: [3], [2,1], [1,2], [1,1,1].
%e A214255 a(4) = 8: [4], [3,1], [2,2], [2,1,1], [1,3], [1,2,1], [1,1,2], [1,1,1,1].
%e A214255 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].
%p A214255 b:= proc(n, i) option remember; `if`(n<1 or i<1, 0,
%p A214255       `if`(n=i, 1, add(b(n-i, i+j), j=-2..2)))
%p A214255     end:
%p A214255 a:= n-> `if`(n=0, 1, add(b(n, j), j=1..n)):
%p A214255 seq(a(n), n=0..50);
%t A214255 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_ *)
%Y A214255 Column k=2 of A214248.
%K A214255 nonn
%O A214255 0,3
%A A214255 _Alois P. Heinz_, Jul 08 2012