

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
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OFFSET

1,2


LINKS

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


FORMULA

T(n,k) = T(1,k) + (n1)*2^k.
T(n,k) = 2*T(n, k1) + (1)^k.
T(n,k) = T(n1,k) + 2^k.
T(n,k) = 2^k * n  A001045(k).
T(n,k) = T(n,k1) +2*T(n,k2).


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



