A091264 Matrix defined by a(n,k) = 2^n + (k-1), read by antidiagonals.

0, 1, 1, 3, 2, 2, 7, 4, 3, 3, 15, 8, 5, 4, 4, 31, 16, 9, 6, 5, 5, 63, 32, 17, 10, 7, 6, 6, 127, 64, 33, 18, 11, 8, 7, 7, 255, 128, 65, 34, 19, 12, 9, 8, 8, 511, 256, 129, 66, 35, 20, 13, 10, 9, 9, 1023, 512, 257, 130, 67, 36, 21, 14, 11, 10, 10, 2047, 1024, 513, 258, 131, 68, 37, 22

Offset: 0

Author

Ross La Haye, Feb 23 2004

Keywords

• easy
• nonn
• tabl

Examples

			{0};
{1,1};
{3,2,2};
{7,4,3,3};
{15,8,5,4,4};
{31,16,9,6,5,5};
{63,32,17,10,7,6,6};
a(5,3) = 34 because 2^5 + (3-1) = 34.
		

Crossrefs

Rows: a(0, k) = A001477(k), a(1, k) = A000027(k+1) etc. etc. Columns: a(n, 0) = A000225(n). a(n, 1) = A000079(n). a(n, 2) = A000051(n). a(n, 3) = A052548(n). a(n, 4) = A062709(n). Diagonals: a(n, n+3) = A052968(n+1). a(n, n+2) = A005126(n). a(n, n+1) = A006127(n). a(n, n) = A052944(n). a(n, n-1) = A083706(n-1). Also note that the sums of the antidiagonals = the partial sums of the main diagonal, i.e., a(n, n).

Programs

Mathematica

Flatten[ Table[ Table[ a[i, n - i], {i, n, 0, -1}], {n, 0, 11}]] (* both from Robert G. Wilson v, Feb 26 2004 *)
Table[a[n, k], {n, 0, 10}, {k, 0, 10}] // TableForm (* to view the table *)

Formula

For k > 0, a(n, k)= a(n, k-1) + 1.

a(n, k) = 2^n + (k-1).

Extensions

More terms from Robert G. Wilson v, Feb 23 2004