The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A280665 Recursive 1-parameter sequence a(n) allowing calculation of the Möbius function. 0
 1, 0, 0, -1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 1, 1, -1, 1, -1, -2, 3, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 1, -2, -1, 0, -1, 3, -1, 1, -1, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 2, 2, -3, -1, 0, 0, 1, 1, -2, 2, -1, 1, -1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,19 COMMENTS This sequence is generated from A266378 by excluding the second recursion parameter. LINKS FORMULA l(n) = floor((1/3)*(81+81*n+3*sqrt(729*n^2+1458*n+1104))^(1/3)-5/(81+81*n+3*sqrt(729*n^2+1458*n+1104))^(1/3)) c(n) = n*(n^2+3*n+8)/6 = A003600(n) K(n) = n - 1 - c(l(n) - 1) T(n,m) are coefficients of A008302 p(n) = c(l(n)-2) u(n) = a(p(n)+K(n)+1) v(n) = a(p(n)+K(n)-l(n)+2) x(n) = a(p(n)+l(n)-1)*T(l(n)-1,l(n)*(l(n)-1)/2-K(n)) a(1) = 1 a(2) = 0 if (l(n)-2 >= K(n) or (1/2)*l(n)*(l(n)-1) < K(n)) then a(n) = 0 else a(n) = u(n)-v(n)-x(n) Möbius(n) = a(c(n-1)+n) A100198(n-2) = a(c(n-1)-n), for n>3. EXAMPLE Möbius(2) = a(c(1)+2) and because the c(1)=2 => a(c(1)+2)= a(4). l(4)=2, K(4)=1 so l(4)-2=K(4) and a(4)=u(4)-v(4)-x(4) p(4)=c(l(4)-2)=c(0)=0 u(4)=a(p(4)+K(4)+1)=a(2)=0 v(4)=a(p(4)+K(4)-l(4)+2)=a(1)=1 x(4)=a(p(4)+l(4)-1)*T(l(4)-1,l(4)*(l(4)-1)/2-K(4))=a(1)*T(1,0)=0, as T(1,0)=0. a(4)=u(4)-v(4)-x(4)=0-1-0=-1. MAPLE l := n->floor((1/3)*(81+81*n+3*sqrt(1104+1458*n+729*n^2))^(1/3)-5/(81+81*n+3*sqrt(1104+1458*n+729*n^2))^(1/3)): c := n->(1/6)*n*(n^2+3*n+8): K := n->n-1-c(l(n)-1): A := (n, z)->z*(product(z^i-1, i = 1 .. n-1)): T := (n, k)->coeff(eval(A(n, z)), z, k): p := n->c(l(n)-2): u := n->a(p(n)+K(n)+1): v := n->a(p(n)+K(n)-l(n)+2): x := n->a(p(n)+l(n)-1)*T(l(n)-1, (1/2)*l(n)*(l(n)-1)-K(n)): a := proc (n) option remember; if K(n) <= l(n)-2 or (1/2)*l(n)*(l(n)-1) < K(n) then 0 else u(n)-v(n)-x(n) end if end proc: a(2) := 0: a(1) := 1: CROSSREFS Cf. A002321, A003600, A008302, A266378. Sequence in context: A316869 A258772 A178401 * A037860 A037878 A107652 Adjacent sequences:  A280662 A280663 A280664 * A280666 A280667 A280668 KEYWORD sign AUTHOR Gevorg Hmayakyan, Jan 06 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 13 19:30 EDT 2020. Contains 336451 sequences. (Running on oeis4.)