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A261962 Number of compositions of n such that no part equals any of its two immediate predecessors.

%I A261962 #12 Dec 03 2020 12:26:58
%S A261962 1,1,1,3,3,5,11,15,23,37,67,101,165,265,419,691,1123,1789,2909,4657,
%T A261962 7515,12183,19657,31635,51101,82449,132989,214623,346485,558587,
%U A261962 901399,1454949,2347157,3787197,6111131,9858931,15908393,25669125,41416849,66826277
%N A261962 Number of compositions of n such that no part equals any of its two immediate predecessors.
%H A261962 Alois P. Heinz, <a href="/A261962/b261962.txt">Table of n, a(n) for n = 0..500</a>
%F A261962 a(n) ~ c * d^n, where d = 1.61350953985228953675390530863679475666564394885974..., c = 0.5270561325668460003703909484716134447490733801644227... - _Vaclav Kotesovec_, Sep 21 2019
%p A261962 b:= proc(n, i, j) option remember; `if`(n=0, 1, add(
%p A261962       `if`(k=i or k=j, 0, (t-> b(t, `if`(k>t, 0, k),
%p A261962       `if`(i>t, 0, i)))(n-k)), k=1..n))
%p A261962     end:
%p A261962 a:= n-> b(n, 0$2):
%p A261962 seq(a(n), n=0..50);
%t A261962 b[n_, i_, j_] := b[n, i, j] = If[n == 0, 1, Sum[If[k == i || k == j, 0, Function[t, b[t, If[k>t, 0, k], If[i>t, 0, i]]][n - k]], {k, 1, n}]];
%t A261962 a[n_] := b[n, 0, 0];
%t A261962 a /@ Range[0, 50] (* _Jean-François Alcover_, Dec 03 2020, after _Alois P. Heinz_ *)
%Y A261962 Column k=2 of A261960.
%Y A261962 Cf. A261961.
%K A261962 nonn
%O A261962 0,4
%A A261962 _Alois P. Heinz_, Sep 06 2015