Stolarsky, Kenneth B. Power and exponential sums of digital sums related to binomial coefficient parity. (English) Zbl 0355.10012 SIAM J. Appl. Math. 32, 717-730 (1977). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 31 Documents MSC: 11A63 Radix representation; digital problems Keywords:Bibliography PDFBibTeX XMLCite \textit{K. B. Stolarsky}, SIAM J. Appl. Math. 32, 717--730 (1977; Zbl 0355.10012) Full Text: DOI Online Encyclopedia of Integer Sequences: 1’s-counting sequence: number of 1’s in binary expansion of n (or the binary weight of n). Total number of 1’s in binary expansions of 0, ..., n. Total number of odd entries in first n rows of Pascal’s triangle: a(0) = 0, a(1) = 1, a(2k) = 3*a(k), a(2k+1) = 2*a(k) + a(k+1). a(n) = Sum_{i=0..n-1} 2^wt(i). Stolarsky-Harborth constant; lim inf_{n->oo} F(n)/n^theta, where F(n) is the number of odd binomial coefficients in the first n rows and theta=log(3)/log(2). a(n) = Sum_{i=0..n} wt(i)^2, where wt(i) = A000120(i). a(n) = Sum_{i=0..n} wt(i)^3, where wt() = A000120().