|
%I #5 Apr 06 2014 04:18:10
%S 1,1,1,2,3,4,7,9,14,19,28,36,53,68,94,122,165,210,280,354,462,583,749,
%T 936,1192,1481,1862,2303,2871,3527,4366,5336,6555,7977,9737,11790,
%U 14317,17260,20845,25033,30093,35993,43087,51348,61216,72711,86362,102236
%N Number of partitions of n such that m(greatest part) <= m(1), where m = multiplicity.
%F a(n) = A240076(n) + A240078(n) for n >= 0.
%e a(7) counts these 9 partitions: 61, 511, 421, 4111, 3211, 31111, 22111, 211111, 1111111.
%t z = 60; f[n_] := f[n] = IntegerPartitions[n]; t1 = Table[Count[f[n], p_ /; Count[p, Max[p]] < Count[p, 1]], {n, 0, z}] (* A240076 *)
%t t2 = Table[Count[f[n], p_ /; Count[p, Max[p]] <= Count[p, 1]], {n, 0, z}] (* A240077 *)
%t t3 = Table[Count[f[n], p_ /; Count[p, Max[p]] == Count[p, 1]], {n, 0, z}] (* A240078 *)
%t t4 = Table[Count[f[n], p_ /; Count[p, Max[p]] > Count[p, 1]], {n, 0, z}] (* A117995 *)
%t t5 = Table[Count[f[n], p_ /; Count[p, Max[p]] >= Count[p, 1]], {n, 0, z}] (* A240080 *)
%Y Cf. A240076, A240078, A117995, A240080.
%K nonn,easy
%O 0,4
%A _Clark Kimberling_, Apr 01 2014
|
