A235804 Rectangular array read by upward antidiagonals: A(n,k) = n-2+k*2^(n-3), n>=3, k>=0.

1, 2, 2, 3, 4, 3, 4, 7, 6, 4, 5, 12, 11, 8, 5, 6, 21, 20, 15, 10, 6, 7, 38, 37, 28, 19, 12, 7, 8, 71, 70, 53, 36, 23, 14, 8, 9, 136, 135, 102, 69, 44, 27, 16, 9, 10, 265, 264, 199, 134, 85, 52, 31, 18, 10, 11, 522, 521, 392, 263, 166, 101, 60, 35, 20, 11

Offset

3,2

Comments

Row index n begins with 3, column index k begins with 0.

Conjectured equivalence classes associated with the row entries of A233332.

Links

Table of n, a(n) for n=3..68.

Formula

Conjecture: G.f. for row n is F_n(x) = ((n-2)+(2^(n-3)-(n-2))*x)/(1-x)^2 = ((n-2)+(2^(n-3)-(n-3)-1)*x)/(1-x)^2 = ((n-2)+A000295(n-3)*x)/(1-x)^2, n>=3.

Conjecture: G.f. for column k is G_k(x) = (k+1-2*(k+1)*x+k*x^2)/((1-2*x)*(1-x)^2), k>=0.

Example

Array begins:
 1,   2,    3,    4,    5,    6,    7,    8,    9,   10, ...
 2,   4,    6,    8,   10,   12,   14,   16,   18,   20, ...
 3,   7,   11,   15,   19,   23,   27,   31,   35,   39, ...
 4,  12,   20,   28,   36,   44,   52,   60,   68,   76, ...
 5,  21,   37,   53,   69,   85,  101,  117,  133,  149, ...
 6,  38,   70,  102,  134,  166,  198,  230,  262,  294, ...
 7,  71,  135,  199,  263,  327,  391,  455,  519,  583, ...
 8, 136,  264,  392,  520,  648,  776,  904, 1032, 1160, ...
 9, 265,  521,  777, 1033, 1289, 1545, 1801, 2057, 2313, ...
10, 522, 1034, 1546, 2058, 2570, 3082, 3594, 4106, 4618, ...

Crossrefs

Cf. A000295, A132925 (conjectured antidiagonal sums), A233332.

Sequence in context: A119457 A241356 A065157 * A051597 A084193 A049787

Adjacent sequences: A235801 A235802 A235803 * A235805 A235806 A235807

Keyword

nonn,tabl

Author

L. Edson Jeffery, Jan 16 2014

Status

approved