login
A182747
Bisection (odd part) of number of partitions that do not contain 1 as a part A002865.
13
0, 1, 2, 4, 8, 14, 24, 41, 66, 105, 165, 253, 383, 574, 847, 1238, 1794, 2573, 3660, 5170, 7245, 10087, 13959, 19196, 26252, 35717, 48342, 65121, 87331, 116600, 155038, 205343, 270928, 356169, 466610, 609237, 792906, 1028764, 1330772, 1716486, 2207851
OFFSET
0,3
COMMENTS
a(n+1) = number of partitions p of 2n such that (number of parts of p) is a part of p, for n >=0. - Clark Kimberling, Mar 02 2014
LINKS
FORMULA
a(n) = p(2*n+1)-p(2*n), where p is the partition function, A000041. - George Beck, Aug 14 2011
MAPLE
b:= proc(n, i) option remember;
if n<0 then 0
elif n=0 then 1
elif i<2 then 0
else b(n, i-1) +b(n-i, i)
fi
end:
a:= n-> b(2*n+1, 2*n+1):
seq(a(n), n=0..40); # Alois P. Heinz, Dec 01 2010
MATHEMATICA
f[n_] := Table[PartitionsP[2 k + 1] - PartitionsP[2 k], {k, 0, n}] (* George Beck, Aug 14 2011 *)
(* also *)
Table[Count[IntegerPartitions[2 n], p_ /; MemberQ[p, Length[p]]], {n, 20}] (* Clark Kimberling, Mar 02 2014 *)
b[n_, i_] := b[n, i] = Which[n<0, 0, n == 0, 1, i<2, 0, True, b[n, i-1] + b[n-i, i]]; a[n_] := b[2*n+1, 2*n+1]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Aug 29 2016, after Alois P. Heinz *)
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Dec 01 2010
EXTENSIONS
More terms from Alois P. Heinz, Dec 01 2010
STATUS
approved