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A235804 Rectangular array read by upward antidiagonals: A(n,k) = n-2+k*2^(n-3), n>=3, k>=0. 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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,tabl
AUTHOR
L. Edson Jeffery, Jan 16 2014
STATUS
approved

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Last modified February 24 02:58 EST 2024. Contains 370288 sequences. (Running on oeis4.)