OFFSET
6,12
COMMENTS
The perimeter is the sum of all parts having less than two neighbors.
a(n) counts all partitions of n into distinct parts where only part 2 has two neighbors.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 6..1000
FORMULA
a(n) = A227344(n,n-2).
EXAMPLE
a(6) = 1: [1,2,3].
a(11) = 1: [1,2,3,5].
a(17) = 2: [1,2,3,5,6], [1,2,3,11].
a(19) = 3: [1,2,3,5,8], [1,2,3,6,7], [1,2,3,13].
a(21) = 4: [1,2,3,7,8], [1,2,3,5,10], [1,2,3,6,9], [1,2,3,15].
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].
MAPLE
b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(i<5, 0,
b(n, i-1, 0)+`if`(i>n or t=2, 0, b(n-i, i-1, t+1))))
end:
a:= n-> b(n-6, n-6, 0):
seq(a(n), n=6..100);
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 17 2013
STATUS
approved