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Irregular triangle read by rows in which row n lists the first n - 2 terms of A000005 together with the sum of A000005(n-1) and A000005(n), with a(1) = 1.
2

%I #12 Jul 27 2021 01:40:15

%S 1,3,1,4,1,2,5,1,2,2,5,1,2,2,3,6,1,2,2,3,2,6,1,2,2,3,2,4,6,1,2,2,3,2,

%T 4,2,7,1,2,2,3,2,4,2,4,7,1,2,2,3,2,4,2,4,3,6,1,2,2,3,2,4,2,4,3,4,8,1,

%U 2,2,3,2,4,2,4,3,4,2,8,1,2,2,3,2,4,2,4,3,4,2,6,6

%N Irregular triangle read by rows in which row n lists the first n - 2 terms of A000005 together with the sum of A000005(n-1) and A000005(n), with a(1) = 1.

%C T(n,k) is the total number of divisors related to the terraces that are in the k-th level that contains terraces starting from the base of the symmetric tower described in A221529.

%e Triangle begins:

%e 1;

%e 3;

%e 1, 4;

%e 1, 2, 5;

%e 1, 2, 2, 5;

%e 1, 2, 2, 3, 6;

%e 1, 2, 2, 3, 2, 6;

%e 1, 2, 2, 3, 2, 4, 6;

%e 1, 2, 2, 3, 2, 4, 2, 7;

%e 1, 2, 2, 3, 2, 4, 2, 4, 7;

%e 1, 2, 2, 3, 2, 4, 2, 4, 3, 6;

%e 1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 8;

%e 1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 8;

%e 1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 6, 6;

%e ...

%Y The length of row n is A028310(n-1).

%Y Row sums give A006218, n >= 1.

%Y Leading diagonal gives A092405.

%Y Other diagonals give A000005.

%Y Column 1 gives the absolute values of A260196.

%Y Companion of A346533.

%Y Cf. A221529, A237270, A237593, A336811, A338156, A340035.

%K nonn,tabf

%O 1,2

%A _Omar E. Pol_, Jul 23 2021