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A360033 Table T(n,k), n >= 1 and k >= 0, read by antidiagonals, related to Jacobsthal numbers A001045. 0
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 (list; table; graph; refs; listen; history; text; internal format)
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: A360029 A360030 A360032 * A360034 A360035 A360036

KEYWORD

nonn,tabl,easy

AUTHOR

Philippe Deléham, Jan 22 2023

STATUS

approved

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Last modified March 31 08:44 EDT 2023. Contains 361645 sequences. (Running on oeis4.)