A059848 As a square table by antidiagonals, the n-digit number which in base k starts 1010101...

0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 2, 2, 0, 0, 1, 3, 5, 2, 1, 0, 1, 4, 10, 10, 3, 0, 0, 1, 5, 17, 30, 21, 3, 1, 0, 1, 6, 26, 68, 91, 42, 4, 0, 0, 1, 7, 37, 130, 273, 273, 85, 4, 1, 0, 1, 8, 50, 222, 651, 1092, 820, 170, 5, 0, 0, 1, 9, 65, 350, 1333, 3255, 4369, 2460, 341, 5, 1, 0, 1, 10

Offset: 0

Author

Henry Bottomley, Feb 26 2001

Keywords

• nonn
• tabl
• base

Examples

			T(5,3)=10101 base 3=81+9+1=91; T(4,6)=1010 base 6=216+6=222. Table starts {0,0,0,0,...}, {1,1,1,1,...}, {0,1,2,3,...}, {1,2,5,10,...}, ...
		

Crossrefs

Rows include A000004, A000012, A001477, A002522, A034262, A059826, A059830, A059839. Columns include A000035, A008619, A000975, A033113, A033114, A033115, A033116, A033117, A033118, A033119, A056830.

Formula

T(n, k)=floor[k^(n+1)/(k^2-1)] =T(n-2, k)+k^(n-1) =k*T(n-1, k)-((-1)^n-1)/2