

A008621


Expansion of 1/((1x)*(1x^4)).


25



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
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OFFSET

0,5


COMMENTS

Arises from Gleason's theorem on selfdual codes: 1/((1x^2)*(1x^8)) is the Molien series for the real 2dimensional Clifford group (a dihedral group of order 16) of genus 1.
Count of odd numbers between consecutive quartersquares, 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
a(n1) is the minimum independence number over all planar graphs with n vertices. The bound follows from the Four Color Theorem. It is attained by a union of 4cliques. Other extremal graphs are examined in the Bickle link.  Allan Bickle, Feb 04 2022


REFERENCES

D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 100.
F. J. MacWilliams and N. J. A. Sloane, Theory of ErrorCorrecting Codes, 1977, Chapter 19, Problem 3, p. 602.


LINKS



FORMULA

a(n) = floor(n/4) + 1.
a(n) = a(n1) + a(n4)  a(n5); a(0)=1, a(1)=1, a(2)=1, a(3)=1, a(4)=2.  Harvey P. Dale, Feb 19 2012
G.f.: 1 / ( (1+x)*(1+x^2)*(x1)^2 ).


MATHEMATICA

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


PROG



CROSSREFS



KEYWORD

nonn,easy,nice


AUTHOR



EXTENSIONS



STATUS

approved



