A101858 Array read by antidiagonals: T(n,k) = Porta-Stolarsky star product T(n,k) = n * k = nk + floor(phi n) floor(phi k) where phi = (1 + sqrt(5))/2.

2, 5, 5, 7, 13, 7, 10, 18, 18, 10, 13, 26, 25, 26, 13, 15, 34, 36, 36, 34, 15, 18, 39, 47, 52, 47, 39, 18, 20, 47, 54, 68, 68, 54, 47, 20, 23, 52, 65, 78, 89, 78, 65, 52, 23, 26, 60, 72, 94, 102, 102, 94, 72, 60, 26, 28, 68, 83, 104, 123, 117, 123, 104, 83, 68, 28, 31, 73, 94, 120

Offset: 1

Author

N. J. A. Sloane, Jan 28 2005

Keywords

• nonn
• tabl

Examples

			..2...5...7..10..13..15..18..20..23..26.
..5..13..18..26..34..39..47..52..60..68.
..7..18..25..36..47..54..65..72..83..94.
.10..26..36..52..68..78..94.104.120.136.
.13..34..47..68..89.102.123.136.157.178.
.15..39..54..78.102.117.141.156.180.204.
.18..47..65..94.123.141.170.188.217.246.
.20..52..72.104.136.156.188.208.240.272.
.23..60..83.120.157.180.217.240.277.314.
.26..68..94.136.178.204.246.272.314.356.
		

Links

• 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

See A101330, A101385, A101633, A101866 for related definitions of product.

Main diagonal is A101863.

First 3 rows are A001950, A101864, A101865.

Cf. A001622.

Programs

Maple

A101858 := proc(n,k)
        phi := (1+sqrt(5))/2 ;
        n*k+floor(n*phi)*floor(phi*k) ;
end proc: # R. J. Mathar, Dec 06 2011

Mathematica

t[n_, k_] := n*k + Floor[n*GoldenRatio] * Floor[GoldenRatio*k]; Table[t[n-k, k], {n, 2, 13}, {k, 1, n-1}] // Flatten (* Jean-François Alcover, Jan 14 2014 *)