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A383026 Triangle T(n,k) read by rows whose n-th row is the lexicographically first n-tuple of ordered distinct positive integers with sum A382547(n) and product A382547(n) * 100^(n-1), or an n-tuple of zeros when A382547(n) = 0.

%I A383026 #18 Jun 20 2025 04:54:24
%S A383026 1,180,225,150,175,200,125,160,175,184,125,127,150,160,200,100,125,
%T A383026 140,150,175,192,80,100,125,150,160,173,250,80,100,110,125,140,150,
%U A383026 200,250,50,100,112,125,150,155,160,200,250,50,80,100,125,128,150,170,175,200,250
%N A383026 Triangle T(n,k) read by rows whose n-th row is the lexicographically first n-tuple of ordered distinct positive integers with sum A382547(n) and product A382547(n) * 100^(n-1), or an n-tuple of zeros when A382547(n) = 0.
%C A383026 Because A382547(n) > 0 for only finitely many n, the triangle has only finitely many nonzero rows.
%H A383026 Markus Sigg, <a href="/A383026/b383026.txt">Table of n, a(n) for n = 1..231</a>, rows 1..21, flattened.
%e A383026 Triangle begins:
%e A383026     1,
%e A383026   180, 225,
%e A383026   150, 175, 200,
%e A383026   125, 160, 175, 184,
%e A383026   125, 127, 150, 160, 200,
%e A383026   100, 125, 140, 150, 175, 192,
%e A383026    80, 100, 125, 150, 160, 173, 250,
%e A383026    80, 100, 110, 125, 140, 150, 200, 250,
%e A383026    50, 100, 112, 125, 150, 155, 160, 200, 250,
%e A383026    50,  80, 100, 125, 128, 150, 170, 175, 200, 250,
%e A383026    50,  65,  75, 100, 125, 128, 150, 175, 200, 250, 320,
%e A383026    25,  50,  80, 100, 125, 128, 150, 200, 225, 230, 250, 300,
%e A383026   ...
%e A383026 For n = 6 there are three 6-tuples with sum A382547(6) = 882 and product 100^5 * 882, namely (100, 125, 140, 150, 175, 192), (100, 125, 147, 150, 160, 200), (112, 120, 125, 150, 175, 200). The first of these is the lexicographically smallest and thus is row 6 of the triangle.
%Y A383026 Cf. A382547, A380887, A381187.
%K A383026 nonn,fini,tabl
%O A383026 1,2
%A A383026 _Markus Sigg_, Apr 13 2025