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%I #19 Jan 18 2025 10:06:43
%S 1,0,1,0,0,2,0,0,0,1,0,0,0,0,2,0,0,0,0,0,2,0,0,0,0,0,0,2,0,0,0,0,0,0,
%T 0,1,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,2,0,0,
%U 0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,2
%N Triangle, diagonal = A001227 with the rest zeros.
%C Lower triangular part of an infinite matrix with A001227 (number of odd divisors of n) as the main diagonal, and the rest filled with zeros. - Redacted from the original formula given by the author. - _Antti Karttunen_, Jan 18 2025
%H Antti Karttunen, <a href="/A133698/b133698.txt">Table of n, a(n) for n = 1..22155; the first 210 rows of the triangle</a>
%e First few rows of the triangle are:
%e 1;
%e 0, 1;
%e 0, 0, 2
%e 0, 0, 0, 1;
%e 0, 0, 0, 0, 2;
%e 0, 0, 0, 0, 0, 2;
%e 0, 0, 0, 0, 0, 0, 2;
%e 0, 0, 0, 0, 0, 0, 0, 1;
%e 0, 0, 0, 0, 0, 0, 0, 0, 3;
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 2;
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2;
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2;
%e ...
%o (PARI)
%o A000265(n) = (n>>valuation(n,2));
%o A133698(n) = if(ispolygonal(n,3), numdiv(A000265((sqrtint(1+(n*8))-1)/2)), 0); \\ _Antti Karttunen_, Jan 18 2025
%Y Cf. A001227, A130209, A133699.
%K nonn,tabl,changed
%O 1,6
%A _Gary W. Adamson_, Sep 21 2007
%E Offset corrected from 0 to 1 and data section extended to a(105) by _Antti Karttunen_, Jan 18 2025