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 A350846 #8 Jan 27 2022 20:47:01
%S A350846 0,0,0,1,1,2,4,5,8,12,18,25,36,48,65,89,119,157,207,269,350,448,574,
%T A350846 729,927,1166,1465,1830,2282,2827,3501,4309,5300,6483,7923,9641,11718,
%U A350846 14187,17155,20674,24885,29860,35787,42772,51054,60791,72289,85772,101641
%N A350846 Number of integer partitions of n with at least two adjacent parts of quotient 2.
%e A350846 The a(3) = 1 through a(9) = 12 partitions:
%e A350846 (21) (211) (221) (42) (421) (422) (63)
%e A350846 (2111) (321) (2221) (521) (621)
%e A350846 (2211) (3211) (3221) (3321)
%e A350846 (21111) (22111) (4211) (4221)
%e A350846 (211111) (22211) (5211)
%e A350846 (32111) (22221)
%e A350846 (221111) (32211)
%e A350846 (2111111) (42111)
%e A350846 (222111)
%e A350846 (321111)
%e A350846 (2211111)
%e A350846 (21111111)
%t A350846 Table[Length[Select[IntegerPartitions[n], MemberQ[Divide@@@Partition[#,2,1],2]&]],{n,0,30}]
%Y A350846 The complement is counted by A350837, strict A350840.
%Y A350846 The complimentary additive version is A350842, strict A350844.
%Y A350846 These partitions are ranked by A350845, complement A350838.
%Y A350846 A000041 = integer partitions.
%Y A350846 A323092 = double-free integer partitions, ranked by A320340.
%Y A350846 Cf. A000929, A003000, A003114, A018819, A045690, A045691, A116931, A120641, A154402, A323093, A342094, A342095, A342096, A342098.
%K A350846 nonn
%O A350846 0,6
%A A350846 _Gus Wiseman_, Jan 20 2022