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A008621 Expansion of 1/((1-x)*(1-x^4)). 20
1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Arises from Gleason's theorem on self-dual codes: 1/((1-x^2)*(1-x^8)) is the Molien series for the real 2-dimensional Clifford group (a dihedral group of order 16) of genus 1.

Count of odd numbers between consecutive quarter-squares, A002620. Oppermann's conjecture states that for each count there will be at least one prime. - Fred Daniel Kline, Sep 10 2011

Number of partitions into parts 1 and 4. - Joerg Arndt, Jun 01 2013

REFERENCES

D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 100.

F. J. MacWilliams and N. J. A. Sloane, Theory of Error-Correcting Codes, 1977, Chapter 19, Problem 3, p. 602.

LINKS

T. D. Noe, Table of n, a(n) for n=0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 211

G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.

Index entries for Molien series

Index to sequences with linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Wikipedia,Oppermann's Conjecture

FORMULA

a(n) = floor((n+3)/4), n>0;

a(n) = A010766(n+4, 4).

a(n) = {sum{k=0..n, (k+1)cos(pi*(n-k)/2}+1/4[cos(n*Pi/2)+1+(-1)^n] }/2 - Paolo P. Lava, Oct 09 2006

Also, a(n) = ceiling((n+1)/4), n >= 0. - Mohammad K. Azarian, May 22 2007

a(n) = sum_{i=0..n} A121262(i) = n/4 +5/8 +(-1)^n/8 + A057077(n)/4. - R. J. Mathar, Mar 14 2011

a(x,y):= floor(x/2)+floor(y/2)-x where x=A002620(n) and y=A002620(n+1), n>2. - Fred Daniel Kline, Sep 10 2011

a(0)=1, a(1)=1, a(2)=1, a(3)=1, a(4)=2, a(n)=a(n-1)+a(n-4)-a(n-5). - Harvey P. Dale, Feb 19 2012

MATHEMATICA

Table[Floor[(n + 3)/4], {n, 1, 80}] (* Stefan Steinerberger, Apr 03 2006 *)

CoefficientList[Series[1/((1-x)(1-x^4)), {x, 0, 80}], x] (* Harvey P. Dale, Feb 19 2012 *)

Flatten[ Table[ PadRight[{}, 4, n], {n, 19}]] (* Harvey P. Dale, Feb 19 2012 *)

CROSSREFS

Cf. A008718, A024186, A110160, A110868, A110869, A110876, A110880.

Cf. A008620, A002265.

Sequence in context: A242601 A110655 * A144075 A128929 A075245 A129253

Adjacent sequences:  A008618 A008619 A008620 * A008622 A008623 A008624

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Stefan Steinerberger, Apr 03 2006

STATUS

approved

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Last modified October 30 09:47 EDT 2014. Contains 248797 sequences.