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A227614 Number of partitions of n into distinct parts with perimeter n-2.

%I A227614 #9 Feb 17 2017 02:33:49
%S A227614 1,0,0,0,0,1,1,1,1,1,1,2,2,3,3,4,4,5,5,7,8,9,11,13,14,17,19,21,25,28,
%T A227614 32,37,42,47,55,61,69,78,88,98,112,124,140,157,176,196,221,245,274,
%U A227614 305,340,377,420,465,517,573,634,702,777,858,949,1047,1154,1273
%N A227614 Number of partitions of n into distinct parts with perimeter n-2.
%C A227614 The perimeter is the sum of all parts having less than two neighbors.
%C A227614 a(n) counts all partitions of n into distinct parts where only part 2 has two neighbors.
%H A227614 Alois P. Heinz, <a href="/A227614/b227614.txt">Table of n, a(n) for n = 6..1000</a>
%F A227614 a(n) = A227344(n,n-2).
%e A227614 a(6) = 1: [1,2,3].
%e A227614 a(11) = 1: [1,2,3,5].
%e A227614 a(17) = 2: [1,2,3,5,6], [1,2,3,11].
%e A227614 a(19) = 3: [1,2,3,5,8], [1,2,3,6,7], [1,2,3,13].
%e A227614 a(21) = 4: [1,2,3,7,8], [1,2,3,5,10], [1,2,3,6,9], [1,2,3,15].
%e A227614 a(23) = 5: [1,2,3,5,12], [1,2,3,6,11], [1,2,3,7,10], [1,2,3,8,9], [1,2,3,17].
%p A227614 b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(i<5, 0,
%p A227614        b(n, i-1, 0)+`if`(i>n or t=2, 0, b(n-i, i-1, t+1))))
%p A227614     end:
%p A227614 a:= n-> b(n-6, n-6, 0):
%p A227614 seq(a(n), n=6..100);
%t A227614 b[n_, i_, t_] := b[n, i, t] = If[n==0, 1, If[i<5, 0, b[n, i-1, 0] + If[i>n || t==2, 0, b[n-i, i-1, t+1]]]]; a[n_] := b[n-6, n-6, 0]; Table[a[n], {n, 6, 100}] (* _Jean-François Alcover_, Feb 17 2017, translated from Maple *)
%Y A227614 Cf. A227344.
%K A227614 nonn
%O A227614 6,12
%A A227614 _Alois P. Heinz_, Jul 17 2013