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A130328 Triangle of differences between powers of 2, read by rows.

%I A130328 #15 Nov 21 2018 02:31:26
%S A130328 1,3,2,7,6,4,15,14,12,8,31,30,28,24,16,63,62,60,56,48,32,127,126,124,
%T A130328 120,112,96,64,255,254,252,248,240,224,192,128,511,510,508,504,496,
%U A130328 480,448,384,256
%N A130328 Triangle of differences between powers of 2, read by rows.
%C A130328 A130321 * A059268 as infinite lower triangular matrices.
%C A130328 Row sums = A000337: (1, 5, 17, 49, 129, 321, ...). A130329 = A059268 * A130321.
%C A130328 From _Alonso del Arte_, Mar 13 2008: (Start)
%C A130328 Column 0 contains the Mersenne numbers A000225.
%C A130328 Column 1 is A000918.
%C A130328 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).
%C A130328 Likewise divisors of multiply perfect numbers, if not the multiply perfect numbers themselves, can also be found in this triangle. (End)
%F A130328 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
%e A130328 First few rows of the triangle are;
%e A130328    1;
%e A130328    3,  2;
%e A130328    7,  6,  4;
%e A130328   15, 14, 12,  8;
%e A130328   31, 30, 28, 24, 16;
%e A130328   63, 62, 60, 56, 48, 32;
%e A130328   ...
%e A130328 a(5, 2) = 28 because 2^5 = 32, 2^2 = 4 and 32 - 4 = 28.
%t A130328 ColumnForm[Table[2^n - 2^k, {n, 15}, {k, 0, n - 1}], Center] (* _Alonso del Arte_, Mar 13 2008 *)
%Y A130328 Cf. A130321, A059268, A000337, A130329.
%K A130328 nonn,tabl
%O A130328 0,2
%A A130328 _Gary W. Adamson_, May 24 2007
%E A130328 Better definition from _Alonso del Arte_, Mar 13 2008