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A240853
Number of partitions p of n into distinct parts including 2*min(p).
2
0, 0, 0, 1, 0, 0, 2, 1, 1, 3, 2, 3, 5, 5, 7, 8, 9, 12, 16, 16, 19, 27, 29, 34, 42, 47, 55, 66, 77, 89, 105, 117, 136, 162, 182, 209, 242, 274, 313, 360, 405, 463, 530, 595, 675, 765, 860, 970, 1099, 1233, 1384, 1559, 1743, 1954, 2191, 2445, 2734, 3057, 3403
OFFSET
0,7
FORMULA
a(n) + A240854(n) = A000009(n) for n >= 0.
EXAMPLE
a(9) counts these 3 partitions: 63, 621, 432.
MATHEMATICA
z = 40; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
Table[Count[f[n], p_ /; MemberQ[p, 2*Min[p]]], {n, 0, z}] (* A240853 *)
Table[Count[f[n], p_ /; !MemberQ[p, 2*Min[p]]], {n, 0, z}] (* A240854 *)
CROSSREFS
Sequence in context: A347584 A366398 A365932 * A363094 A319849 A117334
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 14 2014
STATUS
approved