This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A344650 #12 Aug 05 2021 17:46:59
%S A344650 0,1,1,2,3,5,8,11,16,23,32,44,61,82,111,148,195,256,334,432,557,713,
%T A344650 908,1152,1455,1829,2291,2859,3554,4404,5440,6697,8222,10066,12288,
%U A344650 14964,18176,22023,26625,32117,38656,46432,55661,66592,79523,94793,112792,133984
%N A344650 Number of strict odd-length integer partitions of 2n.
%C A344650 Also the number of strict integer partitions of 2n with reverse-alternating sum >= 0.
%C A344650 Also the number of reversed strict integer partitions of 2n with alternating sum >= 0.
%H A344650 Alois P. Heinz, <a href="/A344650/b344650.txt">Table of n, a(n) for n = 0..2000</a>
%F A344650 Sum of odd-indexed terms in row 2n of A008289.
%F A344650 a(n) = A067659(2n).
%e A344650 The a(1) = 1 through a(8) = 16 partitions:
%e A344650 (2) (4) (6) (8) (10) (12) (14) (16)
%e A344650 (3,2,1) (4,3,1) (5,3,2) (5,4,3) (6,5,3) (7,5,4)
%e A344650 (5,2,1) (5,4,1) (6,4,2) (7,4,3) (7,6,3)
%e A344650 (6,3,1) (6,5,1) (7,5,2) (8,5,3)
%e A344650 (7,2,1) (7,3,2) (7,6,1) (8,6,2)
%e A344650 (7,4,1) (8,4,2) (8,7,1)
%e A344650 (8,3,1) (8,5,1) (9,4,3)
%e A344650 (9,2,1) (9,3,2) (9,5,2)
%e A344650 (9,4,1) (9,6,1)
%e A344650 (10,3,1) (10,4,2)
%e A344650 (11,2,1) (10,5,1)
%e A344650 (11,3,2)
%e A344650 (11,4,1)
%e A344650 (12,3,1)
%e A344650 (13,2,1)
%e A344650 (6,4,3,2,1)
%p A344650 b:= proc(n, i, t) option remember; `if`(n>i*(i+1)/2, 0,
%p A344650 `if`(n=0, t, add(b(n-i*j, i-1, abs(t-j)), j=0..min(n/i, 1))))
%p A344650 end:
%p A344650 a:= n-> b(2*n$2, 0):
%p A344650 seq(a(n), n=0..80); # _Alois P. Heinz_, Aug 05 2021
%t A344650 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&OddQ[Length[#]]&]],{n,0,30,2}]
%Y A344650 The Heinz numbers are the intersection of A030059 and A300061.
%Y A344650 Allowing even length gives A035294 (non-strict: A058696).
%Y A344650 Even bisection of A067659.
%Y A344650 The opposite type of strict partition (even length and odd sum) is A343942.
%Y A344650 The non-strict version is A236559 or A344611.
%Y A344650 Row sums of A344649.
%Y A344650 A000041 counts partitions of 2n with alternating sum 0, ranked by A000290.
%Y A344650 A103919 counts partitions by sum and alternating sum (reverse: A344612).
%Y A344650 A120452 counts partitions of 2n with reverse-alternating sum 2.
%Y A344650 A124754 gives alternating sums of standard compositions (reverse: A344618).
%Y A344650 A152146 interleaved with A152157 counts strict partitions by sum and alternating sum.
%Y A344650 A316524 is the alternating sum of the prime indices of n (reverse: A344616).
%Y A344650 A343941 counts strict partitions of 2n with reverse-alternating sum 4.
%Y A344650 A344604 counts wiggly compositions with twins.
%Y A344650 A344739 counts strict partitions by sum and reverse-alternating sum.
%Y A344650 A344741 counts partitions of 2n with reverse-alternating sum -2.
%Y A344650 Cf. A000070, A000097, A027187, A114121, A239829, A239830, A344607, A344609, A344610, A344651, A344654.
%K A344650 nonn
%O A344650 0,4
%A A344650 _Gus Wiseman_, Jun 05 2021