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A238625
Number of partitions p of n such that 1 + (1/2)*max(p) is a part of p.
1
0, 1, 1, 2, 2, 3, 4, 5, 6, 9, 11, 14, 19, 24, 31, 41, 51, 65, 84, 105, 132, 167, 207, 257, 321, 395, 486, 599, 731, 892, 1089, 1319, 1597, 1933, 2327, 2798, 3361, 4021, 4805, 5736, 6825, 8109, 9625, 11393, 13469, 15905, 18738, 22049, 25915, 30401, 35620
OFFSET
1,4
LINKS
EXAMPLE
a(6) counts these partitions: 222, 2211, 21111.
MATHEMATICA
Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, 1 + Max[p]/2]], {n, 50}]
p[n_, m_] := If[m > n, 0, If[n == m, 1, p[n, m] = Sum[p[n - m, j], {j, m}]]]; a[1] = 0; a[n_] := 1 + Sum[p[n-k-1, 2*k], {k, n/2}]; Array[a, 100] (* Giovanni Resta, Mar 07 2014 *)
CROSSREFS
Sequence in context: A266749 A308283 A336133 * A274145 A036072 A045475
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 02 2014
STATUS
approved