A positive integer n is called balancing number if
1 + 2 + . . . + (n − 1) = (n + 1) + (n + 2) + . . . + (n + r)
holds for some positive integer r. Then r is called balancer corresponding to the balancing number n.
Examples : 6 and 35 are balancing numbers with balancers 2 and 14, respectively.
1 + 2 + 3 + 4 + 5 = 7 + 8
Sequence \( B_n \) of balancing number 0, 1, 6, 35, 204, 1189, 6930, 40391, 235416, 1372105, . . .
\(B_{n} = 6B_{n−1} − B_{n−2}, \), \( B_0 \) = 0 and \( B_1 \) = 1
\( B^2 _{n+1} − B^2 _{n} = B^2 _{n+2} \)
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
