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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 entries for 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. A002265, A008620.

Sequence in context: A242601 A110655 * A144075 A128929 A257839 A075245

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

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 December 9 17:46 EST 2016. Contains 278985 sequences.