

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)(1x^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((4x+2*x^3+x^42*x^52*x^6+2*x^7+3*x^8+2*x^93*x^11)/(1+x^3*(1+xx^7x^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



