0,5

Euler transform of period 6 sequence [0,1,1,1,0,1,...]. - Michael Somos Apr 21 2004

Also number of partitions of n into parts, each larger than 1, such that consecutive integers do not both appear as parts. Example: a(6)=4 because we have [6],[4,2],[3,3] and [2,2,2]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 16 2006

Also number of partitions of n into parts divisible by 2 or 3. - Alexander E. Holroyd (holroyd(AT)math.ubc.ca), May 28 2008

Infinite convolution product of [1,0,1,1,1,1,1] aerated n-1 times. i.e. [1,0,1,1,1,1,1] * [1,0,0,0,1,0,1] * [1,0,0,0,0,0,1] * ... [From Mats Granvik (mats.granvik(AT)abo.fi), Aug 07 2009]

G. E. Andrews, Number Theory, Dover Publications, 1994. page 197. MR1298627

R. Honsberger, Mathematical Gems III, M.A.A., 1985, p. 242.

George E. Andrews, The Theory of Partitions, Addison-Wesley, Reading, Mass., 1976, p. 14, Example 9.

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976 (p. 14, Example 9).

P. A. MacMahon, Combinatory Analysis, Cambridge Univ. Press, London and New York, Vol. 1, 1915 and Vol. 2, 1916; see vol. 2, p 54, Article 300.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

A. E. Holroyd, T. M. Liggett and D. Romik, Integrals, partitions and cellular automata

Eric Weisstein's World of Mathematics, Partition Function P

G.f.: Prod{k>0 is a multiple of 2 or 3} (1/(1-x^k)). - Christian G. Bower (bowerc(AT)usa.net), Jun 23 2000

G.f.: product{i=1, oo, (1+x^3j)/(1-x^2j)} - Jon Perry (perry(AT)globalnet.co.uk), Mar 29 2004

G.f. is a period 1 Fourier series which satisfies f(-1 / (864 t)) = 1/6 (t/i)^(-1/2) g(t) where q = exp(2 pi i t) and g(t) is g.f. for A137566. - Michael Somos, Jan 26 2008

a(6)=4 because we have [3,3],[2,2,2],[2,2,1,1] and [1,1,1,1,1,1].

q + q^49 + q^73 + 2*q^97 + q^121 + 4*q^145 + 2*q^169 + 6*q^193 + ...

1 + x^2 + x^3 + 2*x^4 + x^5 + 4*x^6 + 2*x^7 + 6*x^8 + 5*x^9 + 9*x^10 + ...

G:=product((1-x^j+x^(2*j))/(1-x^j), j=1..70): Gser:=series(G, x=0, 60): 1, seq(coeff(Gser, x^n), n=1..54); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 10 2006

(PARI) a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff(eta(x^6+A)/eta(x^2+A)/eta(x^3+A), n)) /* Michael Somos Apr 21 2004 */

Cf. A000041, A055922, A055923, A114917, A114918.

Sequence in context: A154280 A004795 A161268 this_sequence A143375 A074364 A008796

Adjacent sequences: A007687 A007688 A007689 this_sequence A007691 A007692 A007693

nonn

N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)