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A238548 Number of partitions p of n such that (number of parts of p) - min(p) is not a part of p. 1

%I

%S 1,1,2,3,5,8,12,16,24,32,43,59,79,102,138,179,232,300,388,492,631,794,

%T 1003,1259,1577,1955,2436,3007,3710,4555,5590,6817,8323,10103,12259,

%U 14821,17897,21529,25894,31030,37147,44350,52898,62917,74778,88646,104980

%N Number of partitions p of n such that (number of parts of p) - min(p) is not a part of p.

%F a(n) + A238547(n) = A000041(n).

%e a(6) = 8 counts all 11 partitions of 6 except these: 71, 521, 41111.

%t Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, Length[p]-Min[p]]], {n, 50}]

%o (PARI) a(n) = my(nb = 0); forpart(p=n, if (!vecsearch(Vec(p), #p-vecmin(p)), nb++);); nb; \\ _Michel Marcus_, Jun 18 2015

%Y Cf. A238547.

%K nonn,easy

%O 1,3

%A _Clark Kimberling_, Feb 28 2014

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Last modified February 25 20:52 EST 2020. Contains 332258 sequences. (Running on oeis4.)