This site is supported by donations to The OEIS Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS First quotient=[ n/k ]=Q1; 2nd=[ k/(n-k*Q1) ]; ... Number of squares in a greedy tiling of an n-by-k 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 := a-b*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 A277227 A054531 Adjacent sequences:  A049831 A049832 A049833 * A049835 A049836 A049837 KEYWORD nonn,tabl AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 18 13:09 EST 2019. Contains 319271 sequences. (Running on oeis4.)