The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A088899 T(n, k) = number of ordered pairs of integers (x,y) with x^2/n^2 + y^2/k^2 = 1, 1 <= k <= n; triangular array, read by rows. 3
 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 12, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 12, 4, 4, 4, 4, 12, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 12, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS T(n,k) is the number of lattice points on the circumference of an ellipse with semimajor axis = n, semiminor axis = k and center = (0,0). LINKS Antti Karttunen, Rows n = 1..225 of triangle, flattened Eric Weisstein's World of Mathematics, Ellipse FORMULA a(n) = A088897(n) - A088898(n); T(n,n) = A046109(n). EXAMPLE From Antti Karttunen, Nov 08 2018: (Start) Triangle begins: --------------------------------------------------------------- k=    1   2   3   4   5   6   7   8   9  10  11  12  13  14  15 --------------------------------------------------------------- n= 1: 4; n= 2: 4,  4; n= 3: 4,  4,  4; n= 4: 4,  4,  4,  4; n= 5: 4,  4,  4,  4, 12; n= 6: 4,  4,  4,  4,  4,  4; n= 7: 4,  4,  4,  4,  4,  4,  4; n= 8: 4,  4,  4,  4,  4,  4,  4,  4; n= 9: 4,  4,  4,  4,  4,  4,  4,  4,  4; n=10: 4,  4,  4,  4, 12,  4,  4,  4,  4, 12; n=11: 4,  4,  4,  4,  4,  4,  4,  4,  4,  4,  4; n=12: 4,  4,  4,  4,  4,  4,  4,  4,  4,  4,  4,  4; n=13: 4,  4,  4,  4,  4,  4,  4,  4,  4,  4,  4,  4, 12; n=14: 4,  4,  4,  4,  4,  4,  4,  4,  4,  4,  4,  4,  4,  4; n=15: 4,  4,  4,  4, 12,  4,  4,  4,  4, 12,  4,  4,  4,  4, 12; --- T(5,5) = 12 as there are following 12 solutions for pair (5,5): (5, 0), (4, 3), (3, 4), (0, 5), (-3, 4), (-4, 3), (-5, 0), (-4, -3), (-3, -4), (0, -5), (3, -4), (4, -3). T(15,10) = 12, as there are following 12 solutions for pair (15,10): (-15,0), (-12,-6), (-12,6), (-9,-8), (-9,8), (0,-10), (0,10), (9,-8), (9,8), (12,-6), (12,6), (15,0). (End) PROG (PARI) up_to = 105; A088899tr(n, k) = { my(s=0, t=(n^2)*(k^2)); for(x=-n, n, for(y=-k, k, if((x*x*k*k)+(y*y*n*n) == t, s++))); (s); }; A088899list(up_to) = { my(v = vector(up_to), i=0); for(n=1, oo, for(k=1, n, if(i++ > up_to, return(v)); v[i] = A088899tr(n, k))); (v); }; v088899 = A088899list(up_to); A088899(n) = v088899[n]; \\ Antti Karttunen, Nov 07 2018 CROSSREFS Cf. A046109, A088897, A088898. Sequence in context: A032564 A141248 A273339 * A258199 A290205 A066014 Adjacent sequences:  A088896 A088897 A088898 * A088900 A088901 A088902 KEYWORD nonn,tabl AUTHOR Reinhard Zumkeller, Oct 21 2003 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 September 20 16:50 EDT 2021. Contains 347586 sequences. (Running on oeis4.)