login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A084239 Rank of K-groups of Furstenberg transformation group C*-algebras of n-torus. 3
1, 2, 3, 4, 6, 8, 13, 20, 32, 52, 90, 152, 268, 472, 845, 1520, 2766, 5044, 9277, 17112, 31724, 59008, 110162, 206260, 387282, 729096, 1375654, 2601640, 4929378, 9358944, 17797100, 33904324, 64678112, 123580884, 236413054, 452902072 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 0..500

K. Reihani, C*-algebras from Anzai flows and their K-groups, arXiv preprint arXiv:math/0311425 [math.OA], 2003.

K. Reihani, K-theory of Furstenberg transformation group C^*-algebras, arXiv preprint arXiv:1109.4473 [math.OA], 2011.

FORMULA

a(n) = constant term of prod(i=1, n, 1+t^(i-.5(n+1))) for odd n and a(n) = constant term of (1+t^(.5))*prod(i=1, n, 1+t^(i-.5(n+1))) for even n.

Sums of antidiagonals of A067059, i.e. a(n) is sum over k of number of partitions of [k(n-k)/2] into up to k parts each no more than n-k. Close to 2^(n+1)*sqrt(6/(pi*n^3)) and seems to be even closer to something like 2^(n+1)*sqrt(6/(pi*(n^3+0.9*n^2-0.1825*n+1.5))). - Henry Bottomley, Jul 20 2003

MAPLE

A084239 := proc(n)

    local tt, c ;

    if type(n, 'odd') then

        product( 1+t^(i-(n+1)/2), i=1..n) ;

    else

        (1+t^(1/2))*product( 1+t^(i-(n+1)/2), i=1..n) ;

    end if;

    tt := expand(%) ;

    for c in tt do

        if c = lcoeff(c) then

            return c ;

        end if;

    end do:

end proc: # R. J. Mathar, Nov 13 2016

MATHEMATICA

a[n_] := SeriesCoefficient[If[OddQ[n], 1, 1 + Sqrt[t]]*Product[1 + t^(i - (n + 1)/2), {i, n}], {t, 0, 0}];

Array[a, 36, 0] (* Jean-Fran├žois Alcover, Nov 24 2017 *)

CROSSREFS

Cf. A000980.

Sequence in context: A000029 A155051 A018137 * A283022 A219186 A049708

Adjacent sequences:  A084236 A084237 A084238 * A084240 A084241 A084242

KEYWORD

nonn

AUTHOR

Kamran Reihani (reyhan_k(AT)modares.ac.ir), Jun 21 2003

EXTENSIONS

More terms from Henry Bottomley, Jul 20 2003

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 24 17:19 EST 2018. Contains 299624 sequences. (Running on oeis4.)