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

%I A091264 #21 Aug 01 2015 11:52:05
%S A091264 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,
%T A091264 64,33,18,11,8,7,7,255,128,65,34,19,12,9,8,8,511,256,129,66,35,20,13,
%U A091264 10,9,9,1023,512,257,130,67,36,21,14,11,10,10,2047,1024,513,258,131,68,37,22
%N A091264 Matrix defined by a(n,k) = 2^n + (k-1), read by antidiagonals.
%F A091264 For k > 0, a(n, k)= a(n, k-1) + 1.
%F A091264 a(n, k) = 2^n + (k-1).
%e A091264 {0};
%e A091264 {1,1};
%e A091264 {3,2,2};
%e A091264 {7,4,3,3};
%e A091264 {15,8,5,4,4};
%e A091264 {31,16,9,6,5,5};
%e A091264 {63,32,17,10,7,6,6};
%e A091264 a(5,3) = 34 because 2^5 + (3-1) = 34.
%t A091264 Flatten[ Table[ Table[ a[i, n - i], {i, n, 0, -1}], {n, 0, 11}]] (* both from _Robert G. Wilson v_, Feb 26 2004 *)
%t A091264 Table[a[n, k], {n, 0, 10}, {k, 0, 10}] // TableForm (* to view the table *)
%Y A091264 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).
%K A091264 easy,nonn,tabl
%O A091264 0,4
%A A091264 _Ross La Haye_, Feb 23 2004
%E A091264 More terms from _Robert G. Wilson v_, Feb 23 2004