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A365434 Irregular triangle read by rows: T(n,k) is the number of cubes in the k-th level of the ziggurat of order n described in A347186, n >= 1, k >= 1.

%I A365434 #22 Oct 22 2023 16:57:57
%S A365434 1,3,1,4,2,7,5,3,1,6,4,2,12,9,7,5,3,1,8,6,4,2,15,13,11,9,7,5,3,1,13,9,
%T A365434 7,5,2,18,16,14,12,10,8,6,4,2,12,10,8,6,4,2,28,24,22,20,16,14,12,9,7,
%U A365434 5,3,1,14,12,10,8,6,4,2,24,22,20,18,16,14,12,10,8,6,4,2,24,19,17,15,11,9,7,3,1,1
%N A365434 Irregular triangle read by rows: T(n,k) is the number of cubes in the k-th level  of the ziggurat of order n described in A347186, n >= 1, k >= 1.
%C A365434 The values of n when the number of terms in row n is equal to n give A174973.
%C A365434 The values of n when the number of terms in row n is not equal to n give A238524.
%C A365434 If and only if n is a power of 2 then row n lists the first n odd numbers in decreasing order.
%C A365434 If and only if n is an odd prime then row n lists the first (n + 1)/2 positive even numbers in decreasing order.
%C A365434 If and only if n is an even perfect number then row n lists 2*n together with the first n - 1 odd numbers in decreasing order.
%e A365434 Triangle begins:
%e A365434    1;
%e A365434    3,  1;
%e A365434    4,  2;
%e A365434    7,  5,  3,  1;
%e A365434    6,  4,  2;
%e A365434   12,  9,  7,  5,  3,  1;
%e A365434    8,  6,  4,  2;
%e A365434   15, 13, 11,  9,  7,  5,  3,  1;
%e A365434   13,  9,  7,  5,  2;
%e A365434   18, 16, 14, 12, 10,  8,  6,  4,  2;
%e A365434   12, 10,  8,  6,  4,  2;
%e A365434   28, 24, 22, 20, 16, 14, 12,  9,  7,  5,  3, 1;
%e A365434   14, 12, 10,  8,  6,  4,  2;
%e A365434   24, 22, 20, 18, 16, 14, 12, 10,  8,  6,  4, 2;
%e A365434   24, 19, 17, 15, 11,  9,  7,  3,  1,  1;
%e A365434   31, 29, 27, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1;
%e A365434   ...
%Y A365434 Column 1 gives A000203.
%Y A365434 Row sums give A347186.
%Y A365434 Row lengths give A365433.
%Y A365434 Cf. A000079, A000396, A065091, A174973, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A238524, A245092, A262626, A347263, A347367, A365195.
%K A365434 nonn,tabf
%O A365434 1,2
%A A365434 _Omar E. Pol_, Oct 19 2023