A235803 Rectangular array read by upward antidiagonals: A(n,k) = 1 + sqrt(k)*((1+sqrt(k))^n - (1-sqrt(k))^n)/2, n,k >= 0.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 5, 5, 4, 1, 1, 9, 11, 7, 5, 1, 1, 17, 25, 19, 9, 6, 1, 1, 33, 59, 49, 29, 11, 7, 1, 1, 65, 141, 133, 81, 41, 13, 8, 1, 1, 129, 339, 361, 245, 121, 55, 15, 9, 1, 1, 257, 817, 985, 729, 401, 169, 71, 17, 10, 1

Offset

0,5

Links

Table of n, a(n) for n=0..65.

Formula

A(0,k) = 1, A(n,k) = 1 + k*(sum_{j=0..floor((n-1)/2)} A034867(n,j)*k^j), n>0.

Example

Array begins:
1,   1,    1,    1,     1,     1,     1,      1,      1,      1, ...
1,   2,    3,    4,     5,     6,     7,      8,      9,     10, ...
1,   3,    5,    7,     9,    11,    13,     15,     17,     19, ...
1,   5,   11,   19,    29,    41,    55,     71,     89,    109, ...
1,   9,   25,   49,    81,   121,   169,    225,    289,    361, ...
1,  17,   59,  133,   245,   401,   607,    869,   1193,   1585, ...
1,  33,  141,  361,   729,  1281,  2053,   3081,   4401,   6049, ...
1,  65,  339,  985,  2189,  4161,  7135,  11369,  17145,  24769, ...
1, 129,  817, 2689,  6561, 13441, 24529,  41217,  65089,  97921, ...
1, 257, 1971, 7345, 19685, 43521, 84727, 150641, 250185, 393985, ...
As a triangle:
1;
1,  1;
1,  2,  1;
1,  3,  3,  1;
1,  5,  5,  4,  1;
1,  9, 11,  7,  5,  1;
1, 17, 25, 19,  9,  6, 1;
1, 33, 59, 49, 29, 11, 7, 1; ...

Crossrefs

Cf. A094373 (column k=1)

Sequence in context: A174802 A238346 A053538 * A138201 A220614 A154221

Adjacent sequences: A235800 A235801 A235802 * A235804 A235805 A235806

Keyword

nonn,tabl

Author

L. Edson Jeffery, Jan 15 2014

Status

approved