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URL: https://oeis.org/A227426

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A227426
Number of partitions into distinct parts without three consecutive parts.
2
1, 1, 1, 2, 2, 3, 3, 5, 6, 7, 9, 11, 13, 16, 20, 23, 28, 33, 39, 46, 55, 63, 75, 87, 101, 117, 136, 156, 180, 207, 238, 272, 311, 355, 404, 460, 522, 592, 670, 758, 855, 965, 1087, 1223, 1373, 1543, 1728, 1936, 2166, 2421, 2702, 3016, 3359, 3741, 4162, 4626, 5136, 5702, 6320, 7002, 7753, 8576, 9479, 10473
OFFSET
0,4
COMMENTS
Number of partitions into distinct parts with maximal perimeter.
For n>=1, diagonal of A227344.
LINKS
Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 0..10000
FORMULA
a(n) = c * exp(r*sqrt(n)) / n^(3/4), where r = 1.75931899568... and c = 0.2080626386... - Vaclav Kotesovec, May 24 2018
MAPLE
b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(i<1, 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, n, 0):
seq(a(n), n=0..80); # Alois P. Heinz, Jul 15 2013
MATHEMATICA
b[n_, i_, t_] := b[n, i, t] = If[n==0, 1, If[i<1, 0, b[n, i-1, 0] + If[i>n || t==2, 0, b[n-i, i-1, t+1]]]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 0, 80}] (* Jean-François Alcover, Jul 02 2015, after Alois P. Heinz *)
PROG
(Haskell)
a227426 = p 1 1 where
p _ _ 0 = 1
p k i m = if m < k then 0 else p (k + i) (3 - i) (m - k) + p (k + 1) 1 m
-- Reinhard Zumkeller, Jul 14 2013
CROSSREFS
Cf. A000009.
Sequence in context: A097450 A062303 A180682 * A229950 A388849 A050318
KEYWORD
nonn
AUTHOR
Joerg Arndt, Jul 11 2013
STATUS
approved