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 A005377 Number of low discrepancy sequences in base 4. (Formerly M0504) 5
 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 130, 133, 136, 139 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Harald Niederreiter, Low-discrepancy and low-dispersion sequences, J. Number Theory 30 (1988), no. 1, 51-70. FORMULA Let N(b,n) = (1/n) * Sum_{d|n} mobius(n/d) * b^d. Let M(b,n) = Sum_{k=1..n} N(b,k) with M(b,0) = 0. Let r = r(b,n) be the largest value r such that M(b,r) <= n. Then a(n) = r * (n - M(4, r)) + Sum_{h=1..r} (h-1) * N(4, h) [From Niederreiter paper]. - Sean A. Irvine, Jun 07 2016 G.f.: z^4 * (z^2+1) * (z^4-z^2+1) / (z-1)^2; [Conjectured by Simon Plouffe in his 1992 dissertation, but is incorrect.] MAPLE N := proc(b, n)     option remember;     local d;     add(b^d*numtheory[mobius](n/d), d=numtheory[divisors](n)) ;     %/n ; end proc: M := proc(b, n)     local h;     if n = 0 then         0;     else         add(N(b, h), h=1..n) ;     end if; end proc: nMax := proc(b, s)     local n;     for n from 0 do         if M(b, n) > s then             return n-1 ;         end if;     end do: end proc: A005377 := proc(s)     local n, b;     b := 4 ;     n := nMax(b, s) ;     n*(s-M(b, n))+add( (h-1)*N(b, h), h=1..n) ; end proc: seq(A005377(n), n=1..40) ; # R. J. Mathar, Jun 09 2016 CROSSREFS Cf. A005356 (base 2), A005357 (base 3), A005358 (base 5), A274039 (Plouffe's g.f.) Cf. A001037 (N(2,n)), A027376 (N(3,n)), A027377 (N(4,n)), A062692 (M(2,n)), A114945 (M(3,n)), A114946 (M(4,n)). Sequence in context: A004272 A004279 A274039 * A120370 A011866 A321152 Adjacent sequences:  A005374 A005375 A005376 * A005378 A005379 A005380 KEYWORD nonn,easy AUTHOR EXTENSIONS Terms, offset, and formula corrected by Sean A. Irvine, Jun 07 2016 STATUS approved

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Last modified December 11 07:31 EST 2019. Contains 329914 sequences. (Running on oeis4.)