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 A351005 #9 Feb 10 2022 18:32:22
%S A351005 1,1,2,1,2,2,3,2,4,2,5,4,6,4,8,5,10,6,12,8,16,9,18,12,22,14,28,16,33,
%T A351005 20,40,24,48,28,56,34,67,40,80,46,94,56,110,64,130,75,152,88,176,102,
%U A351005 206,118,238,138,276,159,320,182,368,210,424,242,488,276,558
%N A351005 Number of integer partitions of n into parts that are alternately equal and unequal.
%C A351005 Also partitions whose multiplicities are all 2's, except possibly for the last, which may be 1.
%e A351005 The a(1) = 1 through a(12) = 6 partitions (A..C = 10..12):
%e A351005 1 2 3 4 5 6 7 8 9 A B C
%e A351005 11 22 221 33 331 44 441 55 443 66
%e A351005 2211 332 442 551 552
%e A351005 3311 3322 33221 4422
%e A351005 4411 5511
%e A351005 332211
%t A351005 Table[Length[Select[IntegerPartitions[n],And@@Table[#[[i]]==#[[i+1]],{i,1,Length[#]-1,2}]&&And@@Table[#[[i]]!=#[[i+1]],{i,2,Length[#]-1,2}]&]],{n,0,30}]
%Y A351005 The even-length ordered version is A003242, ranked by A351010.
%Y A351005 The even-length case is A035457.
%Y A351005 Without equalities we have A122135, opposite A122129, even-length A122134.
%Y A351005 The non-strict version is A351004, opposite A351003, even-length A035363.
%Y A351005 The opposite version is A351006, even-length A351007.
%Y A351005 Cf. A000070, A018819, A027383, A088218, A350842, A350844, A351008.
%K A351005 nonn
%O A351005 0,3
%A A351005 _Gus Wiseman_, Jan 31 2022