

A130328


Triangle of differences between powers of 2, read by rows.


4



1, 3, 2, 7, 6, 4, 15, 14, 12, 8, 31, 30, 28, 24, 16, 63, 62, 60, 56, 48, 32, 127, 126, 124, 120, 112, 96, 64, 255, 254, 252, 248, 240, 224, 192, 128, 511, 510, 508, 504, 496, 480, 448, 384, 256
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OFFSET

0,2


COMMENTS

A130321 * A059268 as infinite lower triangular matrices.
Row sums = A000337: (1, 5, 17, 49, 129, 321, ...). A130329 = A059268 * A130321.
From Alonso del Arte, Mar 13 2008: (Start)
Column 0 contains the Mersenne numbers A000225.
Column 1 is A000918.
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. (End)


LINKS

Table of n, a(n) for n=0..44.


FORMULA

t(n, k) = 2^n  2^k, where n is the row number and k 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 zeros)  Alonso del Arte, Mar 13 2008


EXAMPLE

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.


MATHEMATICA

ColumnForm[Table[2^n  2^k, {n, 15}, {k, 0, n  1}], Center] (* Alonso del Arte, Mar 13 2008 *)


CROSSREFS

Cf. A130321, A059268, A000337, A130329.
Sequence in context: A268832 A201566 A072764 * A228993 A083569 A071574
Adjacent sequences: A130325 A130326 A130327 * A130329 A130330 A130331


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, May 24 2007


EXTENSIONS

Better definition from Alonso del Arte, Mar 13 2008


STATUS

approved



