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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A206799 Based on an erroneous version of A008614. 0
4, 1, 0, 2, 4, 3, 4, 4, 4, 5, 4, 6, 8, 7, 8, 8, 8, 9, 12, 10, 12, 15, 12, 12, 16, 17, 16, 18, 20, 19, 20, 20, 24, 25, 24, 26, 28, 27, 28, 32, 32, 33, 36, 34, 36, 39, 40, 40, 44, 45, 44 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

This is based on the formula in Burnside, Section 267, at the foot of page 363. Unfortunately there is a typo in the formula - the term with numerator 21 should have denominator (1+x)(1-x^3). This produces a sequence with 4's in the denominators. Multiplying by 4 gives a sequence of integers, shown here. This is included in the OEIS in accordance with our policy of publishing incorrect sequences together with pointers to the correct versions. - N. J. A. Sloane, Feb 21 2012

REFERENCES

W. Burnside, Theory of Groups of Finite Order, Dover, NY, 1955, section 267, page 363

LINKS

Table of n, a(n) for n=0..50.

FORMULA

A precise definition is: Take the generating function as given by Burnside, expand as a Taylor series, and multiply by 4.

Expansion of (-4 - x + 2 x^3 + x^4 - 2 x^5 - 2 x^6 + 2 x^7 + 3 x^8 + 2 x^9 - 3 x^11)/(-1 + x^3 (1 + x - x^7 - x^8 + x^11))

MATHEMATICA

(* expansion*)

w = Exp[I*2*Pi/7];

p[x_] = FullSimplify[ExpandAll[(4/168)*(1/(1 - x)^3 + 21/((1 - x)*(1 - x^2)) + 42/((1 - x)*(1 + x^2)) + 56/(1 - x^3) + 24/((1 - w*x)*(1 - w^2*x)*(1 - w^4*x)) + 24/((1 - w^6*x)*(1 - x*w^5)*(1 - x*w^3)))]];

a = Table[SeriesCoefficient[Series[FullSimplify[ExpandAll[p[x]]], {x, 0, 50}], n], {n, 0, 50}]

(* recursion*)

b[1] = 4; b[2] = 1; b[3] = 0; b[4] = 2; b[5] = 4; b[6] = 3;

b[7] = 4; b[8] = 4; b[9] = 4; b[10] = 5; b[11] = 4;

b[n_Integer?Positive] :=

b[n] = -489 + 11 n + n^2 - b[-11 + n] - 3 b[-10 + n] - 6 b[-9 + n] -

   9 b[-8 + n] - 11 b[-7 + n] - 12 b[-6 + n] - 12 b[-5 + n] -

   11 b[-4 + n] - 9 b[-3 + n] - 6 b[-2 + n] - 3 b[-1 + n];

Table[b[n], {n, 1, Length[a]}]

PROG

(PARI) Vec((-4-x+2*x^3+x^4-2*x^5-2*x^6+2*x^7+3*x^8+2*x^9-3*x^11)/(-1+x^3*(1+x-x^7-x^8+x^11))+O(x^9)) \\ Charles R Greathouse IV, Feb 13 2012

CROSSREFS

Cf. A008616.

Sequence in context: A249094 A096501 A062862 * A084119 A166073 A290724

Adjacent sequences:  A206796 A206797 A206798 * A206800 A206801 A206802

KEYWORD

dead

AUTHOR

N. J. A. Sloane, Feb 21 2012

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 4 04:39 EDT 2020. Contains 334815 sequences. (Running on oeis4.)