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A241735
Number of partitions p = [x(1), ..., x(k)], where x(1) >= x(2) >= ... >= x(k), of n such that max(x(i) - x(i-1)) is a part of p.
4
0, 0, 0, 1, 1, 2, 4, 5, 7, 10, 15, 19, 28, 34, 46, 61, 81, 101, 137, 168, 218, 273, 349, 431, 550, 676, 849, 1043, 1298, 1579, 1959, 2373, 2913, 3526, 4301, 5178, 6293, 7544, 9109, 10895, 13091, 15591, 18666, 22158, 26402, 31269, 37120, 43813, 51853, 61027
OFFSET
0,6
FORMULA
a(n) + A241736(n) = A000041(n) for n >= 0.
EXAMPLE
a(6) counts these 4 partitions: 42, 321, 2211, 21111.
MATHEMATICA
z = 55; f[n_] := f[n] = IntegerPartitions[n]; g[p_] := Max[-Differences[p]]; g1[p_] := Min[-Differences[p]];
Table[Count[f[n], p_ /; MemberQ[p, g[p]]], {n, 0, z}] (* A241735 *)
Table[Count[f[n], p_ /; ! MemberQ[p, g[p]]], {n, 0, z}] (* A241736 *)
Table[Count[f[n], p_ /; MemberQ[p, g1[p]]], {n, 0, z}] (* A241760 *)
Table[Count[f[n], p_ /; ! MemberQ[p, g1[p]]], {n, 0, z}](* A241761 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 28 2014
STATUS
approved