The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A131130 Binomial transform of [1,1,7,1,7,1,7,1,...]. 11
 1, 2, 10, 26, 58, 122, 250, 506, 1018, 2042, 4090, 8186, 16378, 32762, 65530, 131066, 262138, 524282, 1048570, 2097146, 4194298, 8388602, 16777210, 33554426, 67108858, 134217722, 268435450, 536870906, 1073741818, 2147483642 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For n >= 3, number of vertices of 4,4'-bipyridinium dendrimers (see the Arjomanfar and Gholami reference, p. 71). - Emeric Deutsch, Apr 12 2015 Number of ways to color a (2n-1) X (2n-1) chess board in a "balanced" way. A coloring is called balanced if, within every square subgrid made up of k^2 cells for 1 <= k <= 2*n-1, the number of black cells differs from the number of white cells by at most one. It is problem 3 from the British Maths Olympiad 2020. - Ruediger Jehn, Jan 27 2021 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 A. Arjomanfar and N. Gholami, Computing the Szeged index of 4,4'-bipyridinium dendrimer, Iranian J. Math. Chem., 3, 2012, 67-72. British Mathematical Olympiad, 2020 - Round 2, Problem 3. Index to sequences related to Olympiads. Index entries for linear recurrences with constant coefficients, signature (3,-2). FORMULA Row sums of triangle A131131. a(n) = 4*2^n - 6 for n >= 1; a(0)=1. From Philippe Deléham, Jan 04 2009: (Start) a(n) = 3*a(n-1) - 2*a(n-2), n > 2; a(0)=1, a(1)=2, a(2)=10. G.f.: (1-x+6*x^2) / (1-3*x+2*x^2). (End) a(n) = 2*a(n-1) + 6 for n > 1, a(0)=1, a(1)=2. - Philippe Deléham, Sep 25 2009 E.g.f.: 3 - 6*exp(x) + 4*exp(2*x). - Stefano Spezia, Feb 05 2021 MAPLE 1, seq(4*2^n -6, n = 1..30); MATHEMATICA Join[{1}, LinearRecurrence[{3, -2}, {2, 10}, 30]] (* Harvey P. Dale, Mar 07 2014 *) CoefficientList[Series[(1 -x +6x^2)/(1 -3x +2x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 08 2014 *) CROSSREFS Cf. A095121 (bin transf 1,1,3,1,3,...), A131128 (bin transf 1,1,5,1,5,..), A131131. Sequence in context: A212969 A277712 A009307 * A099969 A241688 A183331 Adjacent sequences: A131127 A131128 A131129 * A131131 A131132 A131133 KEYWORD nonn,easy AUTHOR Gary W. Adamson, Jun 16 2007 EXTENSIONS Edited by Emeric Deutsch, Jul 12 2007 STATUS approved

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

Last modified July 22 22:22 EDT 2024. Contains 374544 sequences. (Running on oeis4.)