A385849 Triangle read by rows: T(n,k) = numerator((Sum_{i=1..k} (n-i+1)^2)/(Sum_{i=1..k} i^2)), with 1 <= k <= n.
1, 4, 1, 9, 13, 1, 16, 5, 29, 1, 25, 41, 25, 9, 1, 36, 61, 11, 43, 18, 1, 49, 17, 55, 21, 27, 139, 1, 64, 113, 149, 29, 38, 199, 29, 1, 81, 29, 97, 23, 51, 271, 2, 71, 1, 100, 181, 35, 49, 6, 355, 53, 95, 128, 1, 121, 221, 151, 61, 83, 451, 17, 41, 167, 101, 1
Offset: 1
Examples
Triangle of the fractions begins as: 1/1; 4/1, 1/1; 9/1, 13/5, 1/1; 16/1, 5/1, 29/14, 1/1; 25/1, 41/5, 25/7, 9/5, 1/1; 36/1, 61/5, 11/2, 43/15, 18/11, 1/1; 49/1, 17/1, 55/7, 21/5, 27/11, 139/91, 1/1; ... T(4,3)/A385850(4,3) = (4^2 + 3^2 + 2^2)/(1^2 + 2^2 + 3^2) = 29/14.
Links
- Stefano Spezia, Table of n, a(n) for n = 1..11325 (first 150 rows of the triangle, flattened)
- Michael De Vlieger, Scatterplot of a(n), n = 1..11325.
Programs
-
Mathematica
T[n_,k_]:=Numerator[(1-3k+2k^2+6n-6k*n+6n^2)/(1+3k+2k^2)]; Table[T[n,k],{n,11},{k,n}]//Flatten
Formula
T(n,k) = numerator((1 - 3*k + 2*k^2 + 6*n - 6*k*n + 6*n^2)/(1 + 3*k + 2*k^2)).