A365434 - OEIS

%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