0,4

Number of 4-block coverings of an n-set where every element of the set is covered by exactly 3 blocks (if offset is 3), so a(n)=(1/4!)*(4^n-6*2^n+8) - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 20 2001

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

J. Goldman and G.-C. Rota, The number of subspaces of a vector space, pp. 75-83 of W. T. Tutte, editor, Recent Progress in Combinatorics. Academic Press, NY, 1969.

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p, 99.

M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.

T. D. Noe, Table of n, a(n) for n=0..200

Index entries for sequences related to linear recurrences with constant coefficients

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

G.f.: x^2/((1-x)(1-2x)(1-4x)).

a(n) = (2^n - 1)*(2^(n-1) - 1)/3 = (1/6)*(4^n) - 2^(n-1) + (1/3).

Row sums of triangle A130324. - Gary W. Adamson (qntmpkt(AT)yahoo.com), May 24 2007

a(n)=stirling2(n,3)+stirling2(n,4), n>=1 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 04 2007

a(n)=sum{k=0..n-1, C(n+k-1,2k)*2^(n-k-1)}+0^n/2. [From Paul Barry (pbarry(AT)wit.ie), Oct 23 2009]

a:=n->sum((4^(n-j)-2^(n-j))/2, j=0..n): seq(a(n), n=-1..23); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 04 2007

with(combinat):seq(stirling2(n, 3)+stirling2(n, 4), n=1..25); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 04 2007

A006095:=-1/(z-1)/(2*z-1)/(4*z-1); [Conjectured by S. Plouffe in his 1992 dissertation.]

(Other) sage: [gaussian_binomial(n, 2, 2) for n in xrange(0, 25)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 24 2009]

First differences: A006516. Cf. also A075113.

Cf. A016208, A000392, A000225, A003462, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125, A016256.

Cf. A130324.

Sequence in context: A022635 A000588 A005285 this_sequence A005003 A163348 A037099

Adjacent sequences: A006092 A006093 A006094 this_sequence A006096 A006097 A006098

nonn,easy,nice

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