A360033 Table T(n,k), n >= 1 and k >= 0, read by antidiagonals, related to Jacobsthal numbers A001045.

1, 2, 1, 3, 3, 3, 4, 5, 7, 5, 5, 7, 11, 13, 11, 6, 9, 15, 21, 27, 21, 7, 11, 19, 29, 43, 53, 43, 8, 13, 23, 37, 59, 85, 107, 85, 9, 15, 27, 45, 75, 117, 171, 213, 171, 10, 17, 31, 53, 91, 149, 235, 341, 427, 341, 11, 19, 35, 61, 107, 181, 299, 469

Offset: 1

Author

Philippe Deléham, Jan 22 2023

Keywords

• nonn
• tabl
• easy

Examples

			The array T(n,k), for n <= 1 and k >= 0, begins:
n = 1: 1,  1,  3,  5,  11,  21,  43, ... -> A001045(k+1)
n = 2: 2,  3,  7, 13,  27,  53, 107, ... -> A048573(k)
n = 3: 3,  5, 11, 21,  43,  85, 171, ... -> A001045(k+3)
n = 4: 4,  7, 15, 29,  59, 117, 235, ... -> ?
n = 5: 5,  9, 19, 37,  75, 149, 299, ... -> A062092(k+1)
n = 6: 6, 11, 23, 45,  91, 181, 363, ... -> ?
n = 7: 7, 13, 27, 53, 107, 213, 427, ... -> A048573(k+2)
		

Crossrefs

Cf. A001045, A048573, A062092.

Columns: A000027, A005408, A004767, A004770, A106839 for k = 0, 1, 2, 3, 4.

Formula

T(n,k) = T(1,k) + (n-1)*2^k.

T(n,k) = 2*T(n, k-1) + (-1)^k.

T(n,k) = T(n-1,k) + 2^k.

T(n,k) = 2^k * n - A001045(k).

T(n,k) = T(n,k-1) +2*T(n,k-2).