OFFSET
1,1
COMMENTS
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..11325 (first 150 antidiagonals, flattened).
P. Arnoux, Some remarks about Fibonacci multiplication, Appl. Math. Lett. 2 (No. 4, 1989), 319-320.
P. Arnoux, Some remarks about Fibonacci multiplication, Appl. Math. Lett. 2 (No. 4, 1989), 319-320. [Annotated scanned copy]
EXAMPLE
The array begins:
3, 6, 8, 11, 14, 16, 19, 21, 24, 27, 29, 32, ...
8, 16, 21, 29, 37, 42, 50, 55, 63, 71, 76, 84, ...
11, 22, 29, 40, 51, 58, 69, 76, 87, 98, 105, 116, ...
16, 32, 42, 58, 74, 84, 100, 110, 126, 142, 152, 168, ...
21, 42, 55, 76, 97, 110, 131, 144, 165, 186, 199, 220, ...
24, 48, 63, 87, 111, 126, 150, 165, 189, 213, 228, 252, ...
29, 58, 76, 105, 134, 152, 181, 199, 228, 257, 275, 304, ...
32, 64, 84, 116, 148, 168, 200, 220, 252, 284, 304, 336, ...
...
MAPLE
T := proc(n, k) local phi;
phi := (1+sqrt(5))/2 ;
n*k+floor(n*phi)*ceil(phi*k) ;
end proc:
for n from 1 to 12 do
lprint([seq(T(n-i+1, i), i=1..n)]);
od: # by antidiagonals
for n from 1 to 12 do
lprint([seq(T(n, i), i=1..12)]);
od: # by rows
MATHEMATICA
A295573[n_, k_] := n*k + Floor[n * GoldenRatio] * Ceiling[k * GoldenRatio];
Table[A295573[n-k+1, k], {n, 15}, {k, n}] (* Paolo Xausa, Mar 20 2024 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Dec 03 2017
STATUS
approved