The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A047470 Numbers that are congruent to {0, 3} mod 8. 20
 0, 3, 8, 11, 16, 19, 24, 27, 32, 35, 40, 43, 48, 51, 56, 59, 64, 67, 72, 75, 80, 83, 88, 91, 96, 99, 104, 107, 112, 115, 120, 123, 128, 131, 136, 139, 144, 147, 152, 155, 160, 163, 168, 171, 176, 179, 184, 187, 192, 195, 200, 203, 208, 211, 216, 219, 224, 227, 232 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Maximum number of squares attacked by a queen on an n X n chessboard. - Stewart Gordon, Mar 23 2001 Equivalently, maximum vertex degree in the n X n queen graph. - Eric W. Weisstein, Jun 20 2017 Number of squares attacked by a queen on a toroidal chessboard. - Diego Torres (torresvillarroel(AT)hotmail.com), May 19 2001 List of squared distances between points of diamond 'lattice' with minimal distance sqrt(3). - Arnold Neumaier (Arnold.Neumaier(AT)univie.ac.at), Aug 01 2003 Draw a figure-eight knot diagram on the plane and assign a list of nonnegative numbers at each crossing as follows. Start with 0 and choose a crossing on the knot. Pick a direction and walk around the knot, appending the following nonnegative number everytime a crossing is visited. Two series of sequences are obtained: this sequence, A047535, A047452, A047617 and A047615, A047461, A047452, A047398 (see example). - Franck Maminirina Ramaharo, Jul 22 2018 LINKS Muniru A Asiru, Table of n, a(n) for n = 1..5000 Eric Weisstein's World of Mathematics, Maximum Vertex Degree Eric Weisstein's World of Mathematics, Queen Graph Index entries for linear recurrences with constant coefficients, signature (1,1,-1). FORMULA a(n) = a(n-1) + 4 + (-1)^n. a(n) = a(n-1) + a(n-2) - a(n-3). a(n) = A042948(n) + A005843(n). G.f.: (3x+5*x^2)/((1-x)*(1-x^2)). a(n) = 8*n - a(n-1) - 13 (with a(1)=0). - Vincenzo Librandi, Aug 06 2010 a(n+1) = Sum_{k>=0} A030308(n,k)*A171497(k). - Philippe Deléham, Oct 17 2011 a(n) = 4*n -(9 + (-1)^n)/2. - Arkadiusz Wesolowski, Sep 18 2012 E.g.f: (10 - exp(-x) + (8*x - 9)*exp(x))/2. - Franck Maminirina Ramaharo, Jul 22 2018 EXAMPLE From Franck Maminirina Ramaharo, Jul 22 2018: (Start) Consider the following equivalent figure-eight knot diagrams: +---------------------+           +-----------------n |                     |           |                 | |           +---------B-----+     |           w-----A---e |           |         |     |     |           |     |   | |     n-----C---+     |     |     |           |     |   | |     |     |   |     |     | <=> |   +-------B-----s   | |     |     +---D-----+     |     |   |       |         | |     |         |           |     |   |       |         | w-----A---------e           |     +---C-------D---------+       |                     |         |       |       s---------------------+         +-------+ Uppercases A,B,C,D denote crossings, and lowercases n,s,w,e denote directions. Due to symmetry and ambient isotopy, all possible sequences are obtained by starting from crossing A and choose either direction 'n' or 's'. Direction 'n': A: 0, 3,  8, 11, 16, 19, 24, 27, 32, 35, 40, ... (this sequence); B: 4, 7, 12, 15, 20, 23, 28, 31, 36, 39, 44, ... A047535; C: 1, 6,  9, 14, 17, 22, 25, 30, 33, 38, 41, ... A047452; D: 2, 5, 10, 13, 18, 21, 26, 29, 34, 37, 42, ... A047617. Direction 's': A: 0, 5,  8, 13, 16, 21, 24, 29, 32, 37, 40, ... A047615; B: 1, 4,  9, 12, 17, 20, 25, 28, 33, 36, 41, ... A047461; C: 2, 7, 10, 15, 18, 23, 26, 31, 34, 39, 42, ... A047524; D: 3, 6, 11, 14, 19, 22, 27, 30, 35, 38, 43, ... A047398. (End) MAPLE a:=n->add(4+(-1)^j, j=1..n):seq(a(n), n=0..64); # Zerinvary Lajos, Dec 13 2008 MATHEMATICA With[{c = 8 Range[0, 30]}, Sort[Join[c, c + 3]]] (* Harvey P. Dale, Oct 11 2011 *) Table[(8 n - 9 - (-1)^n)/2, {n, 20}] (* Eric W. Weisstein, Jun 20 2017 *) LinearRecurrence[{1, 1, -1}, {0, 3, 8}, 20] (* Eric W. Weisstein, Jun 20 2017 *) CoefficientList[Series[(x (3 + 5 x))/((-1 + x)^2 (1 + x)), {x, 0, 20}], x]  (* Eric W. Weisstein, Jun 20 2017 *) PROG (PARI) forstep(n=0, 200, [3, 5], print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011 (GAP) a:=[0, 3, 8];; for n in [4..50] do a[n]:=a[n-1]+a[n-2]-a[n-3]; od; a; # Muniru A Asiru, Jul 23 2018 CROSSREFS Cf. A042948, A047398, A047461, A047452, A047524, A047535, A047615, A047617. Sequence in context: A111132 A188473 A003234 * A184401 A190251 A003623 Adjacent sequences:  A047467 A047468 A047469 * A047471 A047472 A047473 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Vincenzo Librandi, Aug 06 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 10 21:38 EDT 2021. Contains 342856 sequences. (Running on oeis4.)