cp's OEIS Frontend

A347461 Number of distinct possible alternating products of integer partitions of n.

%I A347461 #7 Oct 27 2021 22:22:52
%S A347461 1,1,2,3,4,6,7,10,12,16,19,23,27,34,41,49,57,67,78,91,106,125,147,166,
%T A347461 187,215,245,277,317,357,405,460,524,592,666,740,829,928,1032,1147,
%U A347461 1273,1399,1555,1713,1892,2087,2298,2523,2783,3070,3383,3724,4104,4504
%N A347461 Number of distinct possible alternating products of integer partitions of n.
%C A347461 We define the alternating product of a sequence (y_1,...,y_k) to be Product_i y_i^((-1)^(i-1)).
%e A347461 Partitions representing each of the a(7) = 10 alternating products are:
%e A347461      (7) -> 7
%e A347461     (61) -> 6
%e A347461     (52) -> 5/2
%e A347461    (511) -> 5
%e A347461     (43) -> 4/3
%e A347461    (421) -> 2
%e A347461   (4111) -> 4
%e A347461    (331) -> 1
%e A347461    (322) -> 3
%e A347461   (3211) -> 3/2
%t A347461 altprod[q_]:=Product[q[[i]]^(-1)^(i-1),{i,Length[q]}];
%t A347461 Table[Length[Union[altprod/@IntegerPartitions[n]]],{n,0,30}]
%Y A347461 The version for alternating sum is A004526.
%Y A347461 Counting only integers gives A028310, reverse A347707.
%Y A347461 The version for factorizations is A347460, reverse A038548.
%Y A347461 The reverse version is A347462.
%Y A347461 A000041 counts partitions.
%Y A347461 A027187 counts partitions of even length.
%Y A347461 A027193 counts partitions of odd length.
%Y A347461 A103919 counts partitions by sum and alternating sum (reverse: A344612).
%Y A347461 A108917 counts knapsack partitions, ranked by A299702.
%Y A347461 A122768 counts distinct submultisets of partitions.
%Y A347461 A126796 counts complete partitions.
%Y A347461 A293627 counts knapsack factorizations by sum.
%Y A347461 A301957 counts distinct subset-products of prime indices.
%Y A347461 A304792 counts subset-sums of partitions, positive A276024, strict A284640.
%Y A347461 A304793 counts distinct positive subset-sums of prime indices.
%Y A347461 A325534 counts separable partitions, ranked by A335433.
%Y A347461 A325535 counts inseparable partitions, ranked by A335448.
%Y A347461 Cf. A000070, A001055, A002033, A002219, A028983, A119620, A325768, A345926, A347443, A347444, A347445, A347446.
%K A347461 nonn
%O A347461 0,3
%A A347461 _Gus Wiseman_, Oct 06 2021