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A027197
Number of partitions of n into an even number of parts, the least being 5; also, a(n+5) = number of partitions of n into an odd number of parts, each >=5.
3
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 9, 11, 13, 16, 18, 22, 25, 30, 35, 41, 47, 56, 64, 76, 87, 102, 117, 137, 157, 183, 210, 243, 278, 323, 368, 425, 485, 558, 636, 730, 830, 951, 1081, 1235, 1401, 1598, 1810, 2060
OFFSET
1,20
LINKS
FORMULA
a(n) + A027191(n) = A026798(n). - R. J. Mathar, Oct 18 2019
G.f.: x^10 * Sum_{k>=0} x^(10*k)/Product_{j=1..2*k+1} (1-x^j). - Seiichi Manyama, May 15 2023
MAPLE
b:= proc(n, i, t) option remember; `if`(n=0, t,
`if`(i>n, 0, b(n, i+1, t)+b(n-i, i, 1-t)))
end:
a:= n-> `if`(n<5, 0, b(n-5, 5, 0)):
seq(a(n), n=1..100); # Alois P. Heinz, Oct 18 2019
MATHEMATICA
b[n_, i_, t_] := b[n, i, t] = If[n == 0, t, If[i > n, 0, b[n, i + 1, t] + b[n - i, i, 1 - t]]];
a[n_] := If[n < 5, 0, b[n - 5, 5, 0]];
a /@ Range[100] (* Jean-François Alcover, Feb 06 2020, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A027198 A238215 A237757 * A363221 A332577 A137793
KEYWORD
nonn
STATUS
approved