A131130 Binomial transform of [1,1,7,1,7,1,7,1,...].
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
Offset: 0
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).
Programs
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Maple
1, seq(4*2^n -6, n = 1..30);
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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 *)
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
Extensions
Edited by Emeric Deutsch, Jul 12 2007
Comments