|
%I #22 Oct 22 2023 16:57:57
%S 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 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 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 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 The values of n when the number of terms in row n is equal to n give A174973.
%C The values of n when the number of terms in row n is not equal to n give A238524.
%C If and only if n is a power of 2 then row n lists the first n odd numbers in decreasing order.
%C 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 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 Triangle begins:
%e 1;
%e 3, 1;
%e 4, 2;
%e 7, 5, 3, 1;
%e 6, 4, 2;
%e 12, 9, 7, 5, 3, 1;
%e 8, 6, 4, 2;
%e 15, 13, 11, 9, 7, 5, 3, 1;
%e 13, 9, 7, 5, 2;
%e 18, 16, 14, 12, 10, 8, 6, 4, 2;
%e 12, 10, 8, 6, 4, 2;
%e 28, 24, 22, 20, 16, 14, 12, 9, 7, 5, 3, 1;
%e 14, 12, 10, 8, 6, 4, 2;
%e 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2;
%e 24, 19, 17, 15, 11, 9, 7, 3, 1, 1;
%e 31, 29, 27, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1;
%e ...
%Y Column 1 gives A000203.
%Y Row sums give A347186.
%Y Row lengths give A365433.
%Y Cf. A000079, A000396, A065091, A174973, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A238524, A245092, A262626, A347263, A347367, A365195.
%K nonn,tabf
%O 1,2
%A _Omar E. Pol_, Oct 19 2023
|
