cp's OEIS Frontend

A343942 Number of even-length strict integer partitions of 2n+1.

%I A343942 #8 Jun 12 2021 06:09:08
%S A343942 0,1,2,3,4,6,9,13,19,27,38,52,71,96,128,170,224,292,380,491,630,805,
%T A343942 1024,1295,1632,2049,2560,3189,3959,4896,6038,7424,9100,11125,13565,
%U A343942 16496,20013,24223,29249,35244,42378,50849,60896,72789,86841,103424,122960,145937,172928
%N A343942 Number of even-length strict integer partitions of 2n+1.
%C A343942 By conjugation, also the number of integer partitions of 2n+1 covering an initial interval of positive integers with greatest part even.
%F A343942 The Heinz numbers are A005117 /\ A028260 /\ A300063.
%e A343942 The a(1) = 1 through a(7) = 13 strict partitions:
%e A343942   (2,1)  (3,2)  (4,3)  (5,4)  (6,5)      (7,6)      (8,7)
%e A343942          (4,1)  (5,2)  (6,3)  (7,4)      (8,5)      (9,6)
%e A343942                 (6,1)  (7,2)  (8,3)      (9,4)      (10,5)
%e A343942                        (8,1)  (9,2)      (10,3)     (11,4)
%e A343942                               (10,1)     (11,2)     (12,3)
%e A343942                               (5,3,2,1)  (12,1)     (13,2)
%e A343942                                          (5,4,3,1)  (14,1)
%e A343942                                          (6,4,2,1)  (6,4,3,2)
%e A343942                                          (7,3,2,1)  (6,5,3,1)
%e A343942                                                     (7,4,3,1)
%e A343942                                                     (7,5,2,1)
%e A343942                                                     (8,4,2,1)
%e A343942                                                     (9,3,2,1)
%t A343942 Table[Length[Select[IntegerPartitions[2n+1],UnsameQ@@#&&EvenQ[Length[#]]&]],{n,0,15}]
%Y A343942 Ranked by A005117 (strict), A028260 (even length), and A300063 (odd sum).
%Y A343942 Odd bisection of A067661 (non-strict: A027187).
%Y A343942 The non-strict version is A236914.
%Y A343942 The opposite type of strict partition (odd length and even sum) is A344650.
%Y A343942 A000041 counts partitions of 2n with alternating sum 0, ranked by A000290.
%Y A343942 A103919 counts partitions by sum and alternating sum (reverse: A344612).
%Y A343942 A344610 counts partitions by sum and positive reverse-alternating sum.
%Y A343942 Cf. A000070, A000097, A030229, A035294, A067659, A236559, A338907, A343941, A344649, A344654, A344739.
%K A343942 nonn
%O A343942 0,3
%A A343942 _Gus Wiseman_, Jun 09 2021
%E A343942 More terms from _Bert Dobbelaere_, Jun 12 2021