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!)
 A163433 Number of different fixed (possibly) disconnected trominoes bounded tightly by an n X n square. 7
 0, 4, 22, 52, 94, 148, 214, 292, 382, 484, 598, 724, 862, 1012, 1174, 1348, 1534, 1732, 1942, 2164, 2398, 2644, 2902, 3172, 3454, 3748, 4054, 4372, 4702, 5044, 5398, 5764, 6142, 6532, 6934, 7348, 7774, 8212, 8662, 9124, 9598, 10084, 10582, 11092, 11614 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Except for the first term of 0, a(n) is the set of all integers k such that 6k+12 is a perfect square. - Gary Detlefs, Mar 01 2010 For n > 2, the surface area of a rectangular prism with sides n-2, n-1, and n. - J. M. Bergot, Sep 12 2011 Also the number of 4-cycles in the (n+2) X (n+2) knight graph. - Eric W. Weisstein, May 05 2017 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Graph Cycle Eric Weisstein's World of Mathematics, Knight Graph Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = 6*n^2 - 12*n + 4, n > 1. From Colin Barker, Sep 06 2013: (Start) a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 4. G.f.: 2*x^2*(x^2-5*x-2) / (x-1)^3. (End) a(n+1) = (n*i-1)^3 - (n*i+1)^3, where n > 0, i=sqrt(-1). - Bruno Berselli, Jan 23 2014 E.g.f.: 2*((3*x^2 - 3*x + 2)*exp(x) + x - 2). - G. C. Greubel, Dec 23 2016 EXAMPLE a(2)=4: the four rotations of the (connected) L tromino. MAPLE A163433:=n->6*n^2 - 12*n + 4: 0, seq(A163433(n), n=2..100); # Wesley Ivan Hurt, May 05 2017 MATHEMATICA CoefficientList[Series[(2*z*(z^3 - 5*z^2 - 2*z))/(z - 1)^3, {z, 0, 100}], z] (* Vladimir Joseph Stephan Orlovsky, Jul 17 2011 *) Join[{0}, Table[6*n^2 - 12*n + 4, {n, 2, 50}]] (* G. C. Greubel, Dec 23 2016 *) Join[{0}, LinearRecurrence[{3, -3, 1}, {4, 22, 52}, 50]] (* G. C. Greubel, Dec 23 2016 *) Length /@ Table[FindCycle[KnightTourGraph[n + 2, n + 2], {4}, All], {n, 20}] (* Eric W. Weisstein, May 05 2017 *) PROG (PARI) concat(, Vec(2*x^2*(x^2-5*x-2) / (x-1)^3 + O(x^50))) \\ G. C. Greubel, Dec 23 2016 CROSSREFS Cf. A162673, A163434, A163437. Cf. A289181 (6-cycles in the n X n knight graph). Sequence in context: A297434 A020173 A290709 * A187930 A022603 A050773 Adjacent sequences:  A163430 A163431 A163432 * A163434 A163435 A163436 KEYWORD nonn,easy AUTHOR David Bevan, Jul 28 2009 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 October 17 00:35 EDT 2021. Contains 348048 sequences. (Running on oeis4.)