0,2

A130321 * A059268 as infinite lower triangular matrices.

Row sums = A000337: (1, 5, 17, 49, 129, 321,...). A130329 = A059268 * A130321.

Column 0 contains the Mersenne numbers A000225. - Alonso del Arte (alonso.delarte(AT)gmail.com), Mar 13 2008

Column 1 is A000918. - Alonso del Arte (alonso.delarte(AT)gmail.com), Mar 13 2008

An even perfect number (A000396) is found in the triangle by reference to its matching exponent for the Mersenne prime p (A000043) thus: go to row 2p - 1 and then column p - 1 (remembering that the first position is column 0). Likewise divisors of multiply perfect numbers, if not the multiply perfect numbers themselves, can also be found in this triangle. - Alonso del Arte (alonso.delarte(AT)gmail.com), Mar 13 2008

t(n, k) = 2^n - 2^k, where n is the row number and is the column number, running from 0 to n - 1. (If k is allowed to reach n, then the triangle would have an extra diagonal filled with zeroes) - Alonso del Arte (alonso.delarte(AT)gmail.com), Mar 13 2008

First few rows of the triangle are;

1;

3, 2;

7, 6, 4;

15, 14, 12, 8;

31, 30, 28, 24, 16;

63, 62, 60, 56, 48, 32;

...

a(5, 2) = 28 because 2^5 = 32, 2^2 = 4 and 32 - 4 = 28.

ColumnForm[Table[2^n - 2^k, {n, 15}, {k, 0, n - 1}], Center] - Alonso del Arte (alonso.delarte(AT)gmail.com), Mar 13 2008

Cf. A130321, A059268, A000337, A130329.

Sequence in context: A099896 A006068 A072764 this_sequence A083569 A071574 A054429

Adjacent sequences: A130325 A130326 A130327 this_sequence A130329 A130330 A130331

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), May 24 2007

Better definition from Alonso del Arte (alonso.delarte(AT)gmail.com), Mar 13 2008