A035489 Main diagonal of the Stolarsky array.

1, 6, 18, 39, 81, 157, 309, 576, 1042, 1885, 3338, 6011, 10569, 18321, 31851, 55717, 95320, 163580, 278208, 478807, 814329, 1374926, 2328359, 3963782, 6656320, 11209356, 18772741, 31524784, 53186481, 88750072, 148471480, 247281057, 415039507, 692181268

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

General solution for the Stolarsky array by row, column is given by the PARI/GP program. Solution for the main diagonal in A035506 is found by setting r=c. If computing large terms for the Stolarsky array, increase the default precision of PARI/GP to accommodate the size. - Randall L Rathbun, Jan 25 2002

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..4765
• N. J. A. Sloane, Classic Sequences

Crossrefs

See A007064 for references.

Main diagonal of A035506.

Cf. A001622.

Programs

Maple

a:= proc(n) local t, a, b;
       t:= (1+sqrt(5))/2;
       a:= floor(n*(t+1)+1+t/2);
       b:= round(a*t);
       (<<0|1>, <1|1>>^n. <>)[1, 1]
    end:
seq(a(n), n=0..33);  # Alois P. Heinz, Mar 22 2023

Mathematica

a[n_] := Module[{t = GoldenRatio, a, b},
   a = Floor[n*(t+1) + 1 + t/2];
   b = Round[a*t];
   (MatrixPower[{{0, 1}, {1, 1}}, n].{a, b})[[1]]];
Table[a[n], {n, 0, 33}] (* Jean-François Alcover, Apr 16 2023, after Alois P. Heinz *)

PARI

{Stolarsky(r,c)= tau=(1+sqrt(5))/2; a=floor(r*(1+tau)-tau/2); b=round(a*tau); if(c==1,a, if(c==2,b, for(i=1,c-2,d=a+b; a=b; b=d; ); d))}

Extensions

More terms from Randall L Rathbun, Jan 25 2002