Trollope, J. R. An explicit expression for binary digital sums. (English) Zbl 0162.06303 Math. Mag. 41, 21-25 (1968). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 29 Documents Keywords:number theory PDFBibTeX XMLCite \textit{J. R. Trollope}, Math. Mag. 41, 21--25 (1968; Zbl 0162.06303) 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). a(n) = a(n-1) + sum of digits of n. a(n) = a(n-1) + square of the sum of digits of n. Sum of all digits in ternary expansions of 0, ..., n. 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(). a(n) = Sum_{i=0..n} wt(i)^4, where wt() = A000120(). a(n) = Sum_{i=0..n} digsum_3(i)^2, where digsum_3(i) = A053735(i). a(n) = Sum_{i=0..n} digsum_3(i)^3, where digsum_3(i) = A053735(i). a(n) = Sum_{i=0..n} digsum_3(i)^4, where digsum_3(i) = A053735(i). a(n) = Sum_{i=0..n} digsum_4(i), where digsum_4(i) = A053737(i). a(n) = Sum_{i=0..n} digsum_4(i)^2, where digsum_4(i) = A053737(i). a(n) = Sum_{i=0..n} digsum_4(i)^3, where digsum_4(i) = A053737(i). a(n) = Sum_{i=0..n} digsum_4(i)^4, where digsum_4(i) = A053737(i). a(n) = Sum_{i=0..n} digsum_5(i), where digsum_5(i) = A053824(i). a(n) = Sum_{i=0..n} digsum_5(i)^2, where digsum_5(i) = A053824(i). a(n) = Sum_{i=0..n} digsum_5(i)^3, where digsum_5(i) = A053824(i). a(n) = Sum_{i=0..n} digsum_5(i)^4, where digsum_5(i) = A053824(i). a(n) = Sum_{i=0..n} digsum_6(i), where digsum_6(i) = A053827(i). a(n) = Sum_{i=0..n} digsum_6(i)^2, where digsum_6(i) = A053827(i). a(n) = Sum_{i=0..n} digsum_6(i)^3, where digsum_6(i) = A053827(i). a(n) = Sum_{i=0..n} digsum_6(i)^4, where digsum_6(i) = A053827(i). a(n) = Sum_{i=0..n} digsum_7(i), where digsum_7(i) = A053828(i). a(n) = Sum_{i=0..n} digsum_7(i)^2, where digsum_7(i) = A053828(i). a(n) = Sum_{i=0..n} digsum_7(i)^3, where digsum_7(i) = A053828(i). a(n) = Sum_{i=0..n} digsum_7(i)^4, where digsum_7(i) = A053828(i). a(n) = Sum_{i=0..n} digsum_8(i), where digsum_8(i) = A053829(i). a(n) = Sum_{i=0..n} digsum_8(i)^2, where digsum_8(i) = A053829(i). a(n) = Sum_{i=0..n} digsum_8(i)^3, where digsum_8(i) = A053829(i). a(n) = Sum_{i=0..n} digsum_8(i)^4, where digsum_8(i) = A053829(i). a(n) = Sum_{i=0..n} digsum_9(i), where digsum_9(i) = A053830(i). a(n) = Sum_{i=0..n} digsum_9(i)^2, where digsum_9(i) = A053830(i). a(n) = Sum_{i=0..n} digsum_9(i)^3, where digsum_9(i) = A053830(i). a(n) = Sum_{i=0..n} digsum_9(i)^4, where digsum_9(i) = A053830(i). a(n) = Sum_{i=0..n} digsum(i)^3, where digsum(i) = A007953(i). a(n) = Sum_{i=0..n} digsum(i)^4, where digsum(i) = A007953(i).