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

0,2

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.

Links

Table of n, a(n) for n=0..78.

Formula

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

Example

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.

Sequence in context: A177953 A138895 A138846 * A130321 A101508 A106471

Adjacent sequences: A235667 A235668 A235669 * A235671 A235672 A235673

Keyword

nonn,tabl

Author

Omar E. Pol, Jan 13 2014

Status

approved