A235670 Square array read by antidiagonals upwards in which the n-th column gives the partial sums of the n-th column of A211970.

1, 2, 1, 4, 2, 1, 8, 4, 2, 1, 14, 7, 3, 2, 1, 24, 12, 5, 3, 2, 1, 40, 19, 8, 4, 3, 2, 1, 64, 30, 12, 6, 4, 3, 2, 1, 100, 45, 17, 9, 5, 4, 3, 2, 1, 154, 67, 24, 13, 7, 5, 4, 3, 2, 1, 232, 97, 34, 17, 10, 8, 6, 5, 4, 3, 2, 1, 344, 139, 47, 22, 14, 8, 6, 5, 4, 3, 2, 1

Offset: 0

Author

Omar E. Pol, Jan 13 2014

Keywords

• nonn
• tabl

Comments

The column 0 is related to A008794 in the same way as the column k is related to the generalized (k+4)-gonal numbers, for k >= 1. For more information see A195152 and A211970.

Examples

			Array begins:
1,     1,   1,   1,   1,   1,  1,  1,  1,  1,  1,...
2,     2,   2,   2,   2,   2,  2,  2,  2,  2,  2,...
4,     4,   3,   3,   3,   3,  3,  3,  3,  3,  3,...
8,     7,   5,   4,   4,   4,  4,  4,  4,  4,  4,...
14,   12,   8,   6,   5,   5,  5,  5,  5,  5,  5,...
24,   19,  12,   9,   7,   6,  6,  6,  6,  6,  6,...
40,   30,  17,  13,  10,   8,  7,  7,  7,  7,  7,...
64,   45,  24,  17,  14,  11,  9,  8,  8,  8,  8,...
100,  67,  34,  22,  18,  15, 12, 10,  9,  9,  9,...
154,  97,  47,  29,  22,  19, 16, 13, 11, 10, 10,...
232, 139,  63,  39,  27,  23, 20, 17, 14, 12, 11,...
344, 195,  84,  51,  34,  27, 24, 21, 18, 15, 13,...
504, 272, 112,  65,  44,  32, 28, 25, 22, 19, 16,...
728, 383, 147,  81,  56,  39, 32, 29, 26, 23, 20,...
...
		

Crossrefs

Column 1 is A015128, the partial sums of A211971.

Column 2 is A000070, the partial sums of A000041.

Column 3 is A233969, the partial sums of A006950.

Cf. A000217, A001318, A008794, A085787, A057077, A195152, A211970.

Formula

T(n,k) = Sum_{j=0..n} A211970(j,k), (n>=0, k>=0).