

A049834


Triangular array T given by rows: T(n,k)=sum of quotients when Euclidean algorithm acts on n and k; for k=1,2,...,n; n=1,2,3,...; also number of subtraction steps when computing gcd(n,k) using subtractions rather than divisions.


7



1, 2, 1, 3, 3, 1, 4, 2, 4, 1, 5, 4, 4, 5, 1, 6, 3, 2, 3, 6, 1, 7, 5, 5, 5, 5, 7, 1, 8, 4, 5, 2, 5, 4, 8, 1, 9, 6, 3, 6, 6, 3, 6, 9, 1, 10, 5, 6, 4, 2, 4, 6, 5, 10, 1, 11, 7, 6, 6, 7, 7, 6, 6, 7, 11, 1, 12, 6, 4, 3, 6, 2, 6, 3, 4, 6, 12, 1, 13, 8, 7, 7, 6, 8, 8, 6, 7, 7, 8, 13, 1
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OFFSET

1,2


COMMENTS

First quotient=[ n/k ]=Q1; 2nd=[ k/(nk*Q1) ]; ...
Number of squares in a greedy tiling of an nbyk rectangle by squares. [David Radcliffe, Nov 14 2012]


LINKS

R. J. Mathar, Table of n, a(n) for n = 1..5050
N. J. A. Sloane, Rows 1 through 100


EXAMPLE

Rows:
1;
2,1;
3,3,1;
4,2,4,1;
5,4,4,5,1;
6,3,2,3,6,1;
7,5,5,5,5,7,1;
...


MAPLE

A049834 := proc(n, k)
local a, b, r, s ;
a := n ;
b := k ;
r := 1;
s := 0 ;
while r > 0 do
q := floor(a/b);
r := ab*q ;
s := s+q ;
a := b;
b := r;
end do:
s ;
end proc: # R. J. Mathar, May 06 2016


PROG

(PARI) tabl(nn) = {for (n=1, nn, for (k=1, n, a = n; b = k; r = 1; s = 0; while (r, q = a\b; r = a  b*q; s += q; a = b; b = r); print1(s, ", "); ); print(); ); } \\ Michel Marcus, Aug 17 2015


CROSSREFS

Cf. A049828.
This is the lower triangular part of the square array in A072030.
Sequence in context: A210216 A195915 A219158 * A134625 A325477 A277227
Adjacent sequences: A049831 A049832 A049833 * A049835 A049836 A049837


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling


STATUS

approved



