A081251 Numbers n such that A081249(m)/m^2 has a local maximum for m = n.

2, 6, 20, 60, 182, 546, 1640, 4920, 14762, 44286, 132860, 398580, 1195742, 3587226, 10761680, 32285040, 96855122, 290565366, 871696100, 2615088300, 7845264902, 23535794706, 70607384120, 211822152360, 635466457082, 1906399371246

Offset

1,1

Comments

The limit of the local maxima, lim A081249(n)/n^2 = 1/6. For local minima cf. A081250.

Also the number of different 4- and 3-colorings for the vertices of all triangulated planar polygons on a base with n+2 vertices, if the colors of the two base vertices are fixed. - Patrick Labarque, Mar 23 2010

From Toby Gottfried, Apr 18 2010: (Start)

a(n) = the number of ternary sequences of length n+1 where the numbers of (0's, 1's) are both odd.

A015518 covers the (odd, even) and (even, odd) cases, and A122983 covers (even, even). (End)

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Klaus Brockhaus, Illustration for A081134, A081249, A081250 and A081251

Index entries for linear recurrences with constant coefficients, signature (3,1,-3).

Formula

G.f.: 2/((1-x)*(1+x)*(1-3*x)).

a(n) = a(n-2) + 2*3^(n) for n > 1.

a(n+2) - a(n) = A008776(n).

a(n) = 2*A033113(n+1).

a(2*n+1) = A054880(n+1).

a(n) = floor(3^(n+1)/4). - Mircea Merca, Dec 26 2010

From G. C. Greubel, Jul 14 2019: (Start)

a(n) = (9*3^(n-1) -(-1)^n -2)/4.

E.g.f.: (3*exp(3*x) - 2*exp(x) - exp(-x))/4. (End)

Example

6 is a term since A081249(5)/5^2 = 4/25 = 0.160, A081249(6)/6^2 = 7/36 = 0.194, A081249(7)/7^2 = 9/49 = 0.184.

Maple

seq(floor(3^(n+1)/4), n=1..30). # Mircea Merca, Dec 27 2010

Mathematica

a[n_]:= Floor[3^(n+1)/4]; Array[a, 30]
Table[(9*3^(n-1) -(-1)^n -2)/4, {n, 1, 30}] (* G. C. Greubel, Jul 14 2019 *)

Prog

(Magma) [Floor(3^(n+1)/4) : n in [1..30]]; // Vincenzo Librandi, Jun 25 2011
(PARI) vector(30, n, (9*3^(n-1) -(-1)^n -2)/4) \\ G. C. Greubel, Jul 14 2019
(Sage) [(9*3^(n-1) -(-1)^n -2)/4 for n in (1..30)] # G. C. Greubel, Jul 14 2019
(GAP) List([1..30], n-> (9*3^(n-1) -(-1)^n -2)/4); # G. C. Greubel, Jul 14 2019

Crossrefs

Cf. A008776, A033113, A054880, A081134, A081249, A081250.

Sequence in context: A361732 A005628 A000620 * A134293 A363107 A136883

Adjacent sequences: A081248 A081249 A081250 * A081252 A081253 A081254

Keyword

nonn

Author

Klaus Brockhaus, Mar 17 2003

Status

approved