cp's OEIS Frontend

A357487 Number of integer partitions of n with the same length as reverse-alternating sum.

%I A357487 #5 Oct 02 2022 10:33:35
%S A357487 1,1,0,0,0,1,0,2,0,4,0,5,0,9,0,13,0,23,0,34,0,54,0,78,0,120,0,170,0,
%T A357487 252,0,358,0,517,0,725,0,1030,0,1427,0,1992,0,2733,0,3759,0,5106,0,
%U A357487 6946,0,9345,0,12577,0,16788,0,22384,0,29641,0
%N A357487 Number of integer partitions of n with the same length as reverse-alternating sum.
%C A357487 A partition of n is a weakly decreasing sequence of positive integers summing to n.
%C A357487 The reverse-alternating sum of a sequence (y_1,...,y_k) is Sum_i (-1)^i y_i.
%e A357487 The a(1) = 1 through a(13) = 9 partitions:
%e A357487   1   .  .  .  311   .  322   .  333     .  443     .  553
%e A357487                         421      432        542        652
%e A357487                                  531        641        751
%e A357487                                  51111      52211      52222
%e A357487                                             62111      53311
%e A357487                                                        62221
%e A357487                                                        63211
%e A357487                                                        73111
%e A357487                                                        7111111
%t A357487 ats[y_]:=Sum[(-1)^(i-1)*y[[i]],{i,Length[y]}];
%t A357487 Table[Length[Select[IntegerPartitions[n],Length[#]==ats[Reverse[#]]&]],{n,0,30}]
%Y A357487 For product equal to sum we have A001055, compositions A335405.
%Y A357487 The version for compositions is A357182, reverse ranked by A357184.
%Y A357487 The reverse version is A357189, ranked by A357486.
%Y A357487 These partitions are ranked by A357485.
%Y A357487 Removing zeros gives A357488.
%Y A357487 A000041 counts partitions, strict A000009.
%Y A357487 A025047 counts alternating compositions.
%Y A357487 A103919 counts partitions by alternating sum, full triangle A344651.
%Y A357487 A357136 counts compositions by alternating sum, full triangle A097805.
%Y A357487 Cf. A004526, A051159, A114220, A131044, A262046, A262977, A301987, A357183.
%K A357487 nonn
%O A357487 0,8
%A A357487 _Gus Wiseman_, Oct 01 2022