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A240010
Number of partitions of n, where the difference between the number of odd parts and the number of even parts is 1.
2
1, 0, 1, 1, 1, 2, 2, 4, 3, 7, 6, 11, 11, 17, 19, 27, 31, 41, 51, 62, 79, 95, 121, 142, 182, 212, 269, 314, 393, 459, 570, 665, 816, 958, 1160, 1364, 1639, 1928, 2297, 2706, 3200, 3768, 4434, 5212, 6105, 7170, 8361, 9799, 11396, 13322, 15450, 18022, 20850
OFFSET
1,6
COMMENTS
With offset 2 number of partitions of n, where the difference between the number of odd parts and the number of even parts is -1.
LINKS
EXAMPLE
a(9) = 3: [9], [4,2,1,1,1], [3,2,2,1,1].
a(10) = 7: [8,1,1], [7,2,1], [6,3,1], [5,4,1], [5,3,2], [4,3,3], [2,2,2,1,1,1,1].
MAPLE
b:= proc(n, i, t) option remember; `if`(abs(t)>n, 0,
`if`(n=0, 1, `if`(i<1, 0, b(n, i-1, t)+
`if`(i>n, 0, b(n-i, i, t+(2*irem(i, 2)-1))))))
end:
a:= n-> b(n$2, -1):
seq(a(n), n=1..80);
MATHEMATICA
b[n_, i_, t_] := b[n, i, t] = If[Abs[t] > n, 0, If[n == 0, 1, If[i < 1, 0, b[n, i - 1, t] + If[i > n, 0, b[n - i, i, t + 2 Mod[i, 2] - 1]]]]];
a[n_] := b[n, n, -1];
Array[a, 80] (* Jean-François Alcover, Dec 10 2020, after Alois P. Heinz *)
CROSSREFS
Column k=1 of A240009.
Sequence in context: A325690 A238779 A239832 * A283502 A324756 A373516
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Mar 30 2014
STATUS
approved