OFFSET
0,4
FORMULA
For k > 0, a(n, k)= a(n, k-1) + 1.
a(n, k) = 2^n + (k-1).
EXAMPLE
{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.
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 *)
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).
KEYWORD
AUTHOR
Ross La Haye, Feb 23 2004
EXTENSIONS
More terms from Robert G. Wilson v, Feb 23 2004
STATUS
approved