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A214253 Number of compositions of n where differences between neighboring parts are in {-2,0,2}.

%I A214253 #15 Nov 16 2014 15:08:29
%S A214253 1,1,2,2,5,5,10,10,21,22,42,47,87,103,179,224,380,491,802,1074,1721,
%T A214253 2354,3696,5157,7995,11305,17328,24778,37680,54320,82071,119076,
%U A214253 179061,261046,391087,572275,854975,1254578,1870298,2750361,4093539,6029538,8962963
%N A214253 Number of compositions of n where differences between neighboring parts are in {-2,0,2}.
%H A214253 Alois P. Heinz, <a href="/A214253/b214253.txt">Table of n, a(n) for n = 0..1000</a>
%F A214253 a(n) ~ c * d^n, where d = 1.480632733359847628849916564959539381483927975663120268887..., c = 0.6193575859000249187293498067457554927448225891538342... . - _Vaclav Kotesovec_, Sep 02 2014
%e A214253 a(5) = 5: [5], [3,1,1], [1,3,1], [1,1,3], [1,1,1,1,1].
%e A214253 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].
%p A214253 b:= proc(n, i) option remember; `if`(n<1 or i<1, 0,
%p A214253       `if`(n=i, 1, add(b(n-i, i+j), j=[-2, 0, 2])))
%p A214253     end:
%p A214253 a:= n-> `if`(n=0, 1, add(b(n, j), j=1..n)):
%p A214253 seq(a(n), n=0..60);
%t A214253 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_ *)
%Y A214253 Column k=2 of A214246.
%K A214253 nonn
%O A214253 0,3
%A A214253 _Alois P. Heinz_, Jul 08 2012