cp's OEIS Frontend

A240872 Number of partitions p of n into distinct parts such that max(p) = 4 + min(p).

%I A240872 #13 Jun 18 2025 17:00:28
%S A240872 0,0,0,0,0,0,1,0,2,1,2,2,3,2,2,3,3,2,2,2,4,2,2,2,3,3,2,2,3,2,3,2,3,2,
%T A240872 2,3,3,2,2,2,4,2,2,2,3,3,2,2,3,2,3,2,3,2,2,3,3,2,2,2,4,2,2,2,3,3,2,2,
%U A240872 3,2,3,2,3,2,2,3,3,2,2,2,4,2,2,2,3,3,2,2,3,2,3,2,3,2,2,3,3,2,2,2,4
%N A240872 Number of partitions p of n into distinct parts such that max(p) = 4 + min(p).
%H A240872 Alois P. Heinz, <a href="/A240872/b240872.txt">Table of n, a(n) for n = 0..10000</a>
%H A240872 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1,-1,0,1,1,1,1).
%F A240872 G.f.: -x^6*(x^12+2*x^11+3*x^10+5*x^9+5*x^8+6*x^7+7*x^6+6*x^5+5*x^4+4*x^3+3*x^2+x+1) / ((x-1)*(x+1)*(x^2+1)*(x^4+x^3+x^2+x+1)). - _Alois P. Heinz_, Jun 18 2025
%e A240872 a(12) counts these 3 partitions:  84, 642, 5421.
%t A240872     z = 40; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
%t A240872     Table[Count[f[n], p_ /; Max[p] == 2 + Min[p]], {n, 0, z}] (* A171182 *)
%t A240872     Table[Count[f[n], p_ /; Max[p] == 3 + Min[p]], {n, 0, z}] (* A240871 *)
%t A240872     Table[Count[f[n], p_ /; Max[p] == 4 + Min[p]], {n, 0, z}] (* A240872 *)
%t A240872     Table[Count[f[n], p_ /; Max[p] == 5 + Min[p]], {n, 0, z}] (* A240873 *)
%Y A240872 Cf. A171182, A240871, A240873.
%K A240872 nonn,easy
%O A240872 0,9
%A A240872 _Clark Kimberling_, Apr 15 2014