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 A351006 #12 Feb 04 2022 07:44:09
%S A351006 1,1,1,2,3,4,4,6,7,9,10,12,14,16,18,22,25,28,31,36,40,46,50,56,64,71,
%T A351006 78,88,96,106,118,130,143,158,172,190,209,228,248,274,298,324,354,384,
%U A351006 418,458,494,536,584,631,683,742,800,864,936,1010,1088,1176,1264
%N A351006 Number of integer partitions of n into parts that are alternately unequal and equal.
%e A351006 The a(1) = 1 through a(11) = 12 partitions (A = 10, B = 11):
%e A351006 1 2 3 4 5 6 7 8 9 A B
%e A351006 21 31 32 42 43 53 54 64 65
%e A351006 211 41 51 52 62 63 73 74
%e A351006 311 411 61 71 72 82 83
%e A351006 322 422 81 91 92
%e A351006 511 611 522 433 A1
%e A351006 3221 711 622 533
%e A351006 4221 811 722
%e A351006 32211 5221 911
%e A351006 42211 4331
%e A351006 6221
%e A351006 52211
%t A351006 Table[Length[Select[IntegerPartitions[n],And@@Table[#[[i]]==#[[i+1]],{i,2,Length[#]-1,2}]&&And@@Table[#[[i]]!=#[[i+1]],{i,1,Length[#]-1,2}]&]],{n,0,30}]
%Y A351006 Without equalities we have A122129, opposite A122135, even-length A351008.
%Y A351006 The non-strict version is A351003, opposite A351004, even-length A351012.
%Y A351006 The alternately equal and unequal version is A351005, even-length A035457.
%Y A351006 The even-length case is A351007.
%Y A351006 Cf. A000070, A003242, A018819, A027383, A035363, A088218, A122134, A344605, A350842, A350844, A351011.
%K A351006 nonn
%O A351006 0,4
%A A351006 _Gus Wiseman_, Jan 31 2022