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

0,2

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

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. <<a, b>>)[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 *)

Prog

(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))}

Crossrefs

See A007064 for references.

Main diagonal of A035506.

Cf. A001622.

Sequence in context: A370349 A271252 A271541 * A219143 A122061 A333713

Adjacent sequences: A035486 A035487 A035488 * A035490 A035491 A035492

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Randall L Rathbun, Jan 25 2002

Status

approved