A240873 Number of partitions p of n into distinct parts such that max(p) = 5 + min(p).

0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 2, 3, 3, 3, 4, 4, 4, 5, 4, 3, 6, 4, 4, 5, 3, 4, 6, 4, 4, 4, 4, 4, 6, 4, 3, 5, 4, 4, 6, 3, 4, 5, 4, 4, 5, 4, 4, 5, 4, 3, 6, 4, 4, 5, 3, 4, 6, 4, 4, 4, 4, 4, 6, 4, 3, 5, 4, 4, 6, 3, 4, 5, 4, 4, 5, 4, 4, 5, 4, 3

Offset: 0

Author

Clark Kimberling, Apr 15 2014

Keywords

• nonn
• easy

Examples

			a(12) counts these 3 partitions:  732, 651, 6321.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (-1,-1,-1,-1,0,1,1,1,1,1).

Crossrefs

Cf. A171182, A240871, A240872.

Programs

Mathematica

z = 40; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@Split@#] == 1 &];
Table[Count[f[n], p_ /; Max[p] == 2 + Min[p]], {n, 0, z}] (* A171182 *)
Table[Count[f[n], p_ /; Max[p] == 3 + Min[p]], {n, 0, z}] (* A240871 *)
Table[Count[f[n], p_ /; Max[p] == 4 + Min[p]], {n, 0, z}] (* A240872 *)
Table[Count[f[n], p_ /; Max[p] == 5 + Min[p]], {n, 0, z}] (* A240873 *)