A238708 - OEIS

%I #17 Jan 01 2022 17:55:35

%S 0,0,0,1,0,1,1,2,2,3,4,5,6,8,10,13,15,19,23,28,33,41,48,58,68,81,95,

%T 113,131,154,179,209,241,281,323,374,429,494,565,649,739,845,961,1095,

%U 1241,1411,1595,1807,2039,2303,2593,2923,3283,3691,4139,4643,5195

%N Number of strict partitions of n that include a pair of consecutive integers.

%C Column 2 of the array at A238709.

%C Column k=1 of A238354. - _Alois P. Heinz_, May 02 2014

%H Alois P. Heinz, <a href="/A238708/b238708.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A000009(n) - A003114(n). - _George Beck_, Jan 01 2022

%e a(10) = 4 counts these partitions: 721, 541, 532, 4321.

%t PartitionsQ[Range[50]] - Table[Count[IntegerPartitions[n], p_ /; Min[p] >= Length[p]], {n, 50}]

%Y Cf. A238709, A000009, A238354.

%K nonn,easy

%O 0,8

%A _Clark Kimberling_, Mar 03 2014