0,2

Also Schoenheim bound L_1(n,5,4).

Degrees of polynomials defined by p(n)=(x^(n+1)*p(n-1)p(n-3)+p(n-2)^2)/p(n-4), p(-4)=p(-3)=p(-2)=p(-1)=1. - Michael Somos, Jul 21 2004

Degrees of polynomial tau-functions of q-discrete Painleve I, which generate sequence A095708 when q=2 (up to an offset of 3). - Andrew Hone (anwh(AT)kent.ac.uk), Jul 29 2004

Because of the Laurent phenomenon for the general q-discrete Painleve I tau-function recurrence p(n)=(a*x^(n+1)*p(n-1)*p(n-3)+b*p(n-2)^2)/p(n-4), p(n) for n>-1 will always be a polynomial in x and a Laurent polynomial in a,b and the initial data p[ -4],p[ -3],p[ -2],p[ -1]. - Andrew Hone (anwh(AT)kent.ac.uk), Jul 29 2004

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

H. R. Henze and C. M. Blair, The number of structurally isomeric hydrocarbons of the ethylene series, J. Amer. Chem. Soc., 55 (1933), 680-685.

W. H. Mills and R. C. Mullin, Coverings and packings, pp. 371-399 of J. H. Dinitz and D. R. Stinson, editors,a Contemporary Design Theory, Wiley, 1992. See Eq. 1.

L. Smiley, Hidden Hexagons, (preprint)

S. Fomin and A. Zelevinsky, The Laurent phenomenon, Advances in Applied Mathematics 28 (2002) 119-144.

Brian OSullivan and Thomas Busch, Spontaneous emission in ultra-cold spin-polarised anisotropic Fermi seas, arXiv 0810.0231v1 [quant-ph], 2008. [Eq 10a, lambda=3]

Index entries for two-way infinite sequences

Index entries for covering numbers

A. N. W. Hone, Algebraic curves, integer sequences and a discrete Painleve transcendent, Proceedings of SIDE 6, Helsinki, Finland, 2004. [Set a(n)=d(n+3) on p. 8]

G.f.: 1/((1-x)^3*(1-x^3)). a(n)=-a(-6-n)=3a(n-1)-3a(n-2)+2a(n-3)-3a(n-4)+3a(n-5)-a(n-6).

The simplest recurrence is fourth order: a(n)=a(n-1)+a(n-3)-a(n-4)+n+1, which gives the G.f. 1/((1-x)^3(1-x^3)), with a(-4)=a(-3)=a(-2)=a(-1)=0. An explicit formula is a(n)=n^3/18+n^2/2+4*n/3+1+2/(9*sqrt(3))*sin(2*Pi*n/3). - Andrew Hone (anwh(AT)kent.ac.uk), Jul 29 2004

a(n)=[2*A000027(n+1)+3*A000292(n+1)+A049347(n-1)+1+3*A000217(n+1)]/9. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 16 2007

Polynomials p(0)=x+1, p(1)=x^3+x^2+1, p(2)=x^6+x^5+x^3+x^2+2x+1, ...

L := proc(v, k, t, l) local i, t1; t1 := l; for i from v-t+1 to v do t1 := ceil(t1*i/(i-(v-k))); od: t1; end; # gives Schoenheim bound L_l(v, k, t). Current sequence is L_1(n, n-3, n-4, 1).

(PARI) a(n)=if(n<-5, -a(-6-n), polcoeff(1/(1-x)^3/(1-x^3)+x^n*O(x), n)) /* Michael Somos, Jul 21 2004 */

Cf. A014126, A000631.

A column of A036838.

Cf. A095708.

Sequence in context: A140126 A140235 A010000 this_sequence A147456 A011849 A095944

Adjacent sequences: A014122 A014123 A014124 this_sequence A014126 A014127 A014128

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 24 1999