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

1,2

Links

Table of n, a(n) for n=1..63.

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).

Example

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.

Sequence in context: A105637 A029161 A035384 * A303974 A153868 A341147

Adjacent sequences: A360030 A360031 A360032 * A360034 A360035 A360036

Keyword

nonn,tabl,easy

Author

Philippe Deléham, Jan 22 2023

Status

approved