A295573 Array read by upwards antidiagonals: T(n,k) = nk + floor(phi n) ceiling(phi k) where phi = (1 + sqrt(5))/2.

3, 8, 6, 11, 16, 8, 16, 22, 21, 11, 21, 32, 29, 29, 14, 24, 42, 42, 40, 37, 16, 29, 48, 55, 58, 51, 42, 19, 32, 58, 63, 76, 74, 58, 50, 21, 37, 64, 76, 87, 97, 84, 69, 55, 24, 42, 74, 84, 105, 111, 110, 100, 76, 63, 27, 45, 84, 97, 116, 134, 126, 131, 110, 87, 71, 29, 50, 90, 110, 134, 148, 152, 150, 144, 126, 98, 76, 32

Offset: 1

Author

N. J. A. Sloane, Dec 03 2017

Keywords

• nonn
• tabl

Comments

This is a hybrid of the Porta-Stolarsky star product (A101858) and the Arnoux product (A101866)

Examples

			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, ...
...
		

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]

Crossrefs

Cf. A001622, A101858, A101866, A371382 (main diagonal).

Programs

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 *)