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A325232
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Number of integer partitions (of any nonnegative integer) whose sum minus the lesser of their maximum part and their number of parts is n.
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8
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2, 3, 6, 10, 18, 27, 44, 64, 97, 138, 200, 276, 390, 528, 724, 968, 1301, 1712, 2266, 2946, 3842, 4947, 6372, 8122, 10362, 13094, 16544, 20754, 26010, 32392, 40308, 49876, 61648, 75845, 93178, 114006, 139308, 169586, 206158, 249814, 302267, 364664, 439330
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OFFSET
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0,1
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LINKS
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FORMULA
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For n > 0, a(n) = Sum_{k > 0} A325227(n + k, k).
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EXAMPLE
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The a(0) = 1 through a(4) = 18 partitions:
() (2) (3) (4) (5)
(1) (11) (22) (32) (33)
(21) (31) (41) (42)
(111) (221) (51)
(211) (321) (222)
(311) (411) (322)
(1111) (331)
(2111) (421)
(3111) (511)
(4111) (2211)
(3211)
(4211)
(5111)
(11111)
(21111)
(31111)
(41111)
(51111)
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MATHEMATICA
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nn=30;
mindif[ptn_]:=If[ptn=={}, 0, Total[ptn]-Min[Length[ptn], Max[ptn]]];
allip=Array[IntegerPartitions, 2*nn+2, 0, Join];
Table[Length[Select[allip, mindif[#]==n&]], {n, 0, nn}]
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CROSSREFS
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Number of times n appears in A325224.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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