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%I #19 Mar 20 2024 17:50:59
%S 2,5,5,7,13,7,10,18,18,10,13,26,25,26,13,15,34,36,36,34,15,18,39,47,
%T 52,47,39,18,20,47,54,68,68,54,47,20,23,52,65,78,89,78,65,52,23,26,60,
%U 72,94,102,102,94,72,60,26,28,68,83,104,123,117,123,104,83,68,28,31,73,94,120
%N 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.
%H P. Arnoux, <a href="http://dx.doi.org/10.1016/0893-9659(89)90078-5">Some remarks about Fibonacci multiplication</a>, Appl. Math. Lett. 2 (No. 4, 1989), 319-320.
%H P. Arnoux, <a href="/A101858/a101858.pdf">Some remarks about Fibonacci multiplication</a>, Appl. Math. Lett. 2 (No. 4, 1989), 319-320. [Annotated scanned copy]
%e ..2...5...7..10..13..15..18..20..23..26.
%e ..5..13..18..26..34..39..47..52..60..68.
%e ..7..18..25..36..47..54..65..72..83..94.
%e .10..26..36..52..68..78..94.104.120.136.
%e .13..34..47..68..89.102.123.136.157.178.
%e .15..39..54..78.102.117.141.156.180.204.
%e .18..47..65..94.123.141.170.188.217.246.
%e .20..52..72.104.136.156.188.208.240.272.
%e .23..60..83.120.157.180.217.240.277.314.
%e .26..68..94.136.178.204.246.272.314.356.
%p A101858 := proc(n,k)
%p phi := (1+sqrt(5))/2 ;
%p n*k+floor(n*phi)*floor(phi*k) ;
%p end proc: # _R. J. Mathar_, Dec 06 2011
%t 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 *)
%Y See A101330, A101385, A101633, A101866 for related definitions of product.
%Y Main diagonal is A101863.
%Y First 3 rows are A001950, A101864, A101865.
%Y Cf. A001622.
%K nonn,tabl
%O 1,1
%A _N. J. A. Sloane_, Jan 28 2005
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