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A028399 a(n) = 2^n - 4. 26
0, 4, 12, 28, 60, 124, 252, 508, 1020, 2044, 4092, 8188, 16380, 32764, 65532, 131068, 262140, 524284, 1048572, 2097148, 4194300, 8388604, 16777212, 33554428, 67108860, 134217724, 268435452, 536870908, 1073741820, 2147483644 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

Number of permutations of [n] with 2 sequences.

Number of 2 X n binary matrices that avoid simultaneously the right angled numbered polyomino patterns (ranpp) (00;1) and (11;0). An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i1<i2, j1<j2 and these elements are in same relative order as those in the triple (x,y,z). - Sergey Kitaev (kitaev(AT)ms.uky.edu), Nov 11 2004

The number of edges in the dual Edwards-Venn diagram graph with n-1 digits when n>2.

a(n) (n>=6) is the number of vertices in the molecular graph NS2[n-5], defined pictorially in the Ashrafi et al. reference (Fig. 2, where NS2[2] is shown). - Emeric Deutsch, May 16 2018

REFERENCES

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 261.

A. W. F. Edwards, Cogwheels of the Mind, Johns Hopkins University Press, 2004, p. 82.

LINKS

Muniru A Asiru, Table of n, a(n) for n = 2..700

Ali Reza Ashrafi and Parisa Nikzad, Kekulé index and bounds of energy for nanostar dendrimers, Digest J. of Nanomaterials and Biostructures, 4, No. 2, 2009, 383-388.

S. Kitaev, On multi-avoidance of right angled numbered polyomino patterns, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.

S. Kitaev, On multi-avoidance of right angled numbered polyomino patterns, University of Kentucky Research Reports (2004).

László Németh, Pascal pyramid in the space H^2 x R, arXiv:1701.06022 [math.CO], 2017 (3rd line of Table 2 is a(n+1)).

I. Strazdins, Universal affine classification of Boolean functions, Acta Applic. Math. 46 (1997), 147-167.

Index entries for linear recurrences with constant coefficients, signature (3,-2).

FORMULA

O.g.f.: 4x^3/((1-x)(1-2x)). - R. J. Mathar, Aug 07 2008

From Reinhard Zumkeller, Feb 28 2010: (Start)

a(n) = A175164(2*n)/A140504(n+2);

a(2*n) = A052548(n)*A000918(n) for n > 0;

a(n) = A173787(n,2). (End)

a(n) = a(n-1) + 2^(n-1) (with a(2)=0). - Vincenzo Librandi, Nov 22 2010

a(n) = 4*A000225(n-2). - R. J. Mathar, Dec 15 2015

MAPLE

seq(2^n-4, n=2..40); # Muniru A Asiru, May 17 2018

PROG

(PARI) a(n)=if(n<2, 0, 2^n-4)

(GAP) a:=List([2..40], n->2^n-4); # Muniru A Asiru, May 17 2018

CROSSREFS

Sequence in context: A179023 A269712 * A173033 A317233 A034508 A173380

Adjacent sequences:  A028396 A028397 A028398 * A028400 A028401 A028402

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Additional comments from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Dec 02 2001

STATUS

approved

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Last modified August 15 20:49 EDT 2018. Contains 313779 sequences. (Running on oeis4.)