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A081254 Numbers n such that A081252(m)/m^2 has a local maximum for m = n. 13
1, 3, 6, 13, 26, 53, 106, 213, 426, 853, 1706, 3413, 6826, 13653, 27306, 54613, 109226, 218453, 436906, 873813, 1747626, 3495253, 6990506, 13981013, 27962026, 55924053, 111848106, 223696213, 447392426, 894784853, 1789569706, 3579139413 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The limit of the local maxima, lim A081252(n)/n^2 = 1/10. For local minima cf. A081253.

Row sums of the triangle A181971. - Reinhard Zumkeller, Jul 09 2012

LINKS

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

Klaus Brockhaus, Illustration for A053646, A081252, A081253 and A081254

FORMULA

a(n) = floor(2^n*5/3)

a(n) = a(n-2) + 5*2^(n-2) for n > 1; a(n+2) - a(n) = A020714(n); a(n) + a(n-1) = A052549(n) for n > 0; a(2n) = A020989(n); a(2n+1) = A072197(n); a(n+1) - a(n) = A048573(n);

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

a(n)=5*2^n/3-(-1)^n/6-1/2. a(n)=2a(n-1)+(1-(-1)^n)/2, a(0)=1. - Paul Barry, Mar 24 2003

a(2n)=2*a(2n-1), a(2n+1)=2*a(2n)+1, a(0)=1 . a(n)=A000975(n)+2^n . - Philippe Deléham, Oct 15 2006

EXAMPLE

13 is a term since A081252(12)/12^2 = 15/144 = 0.104, A081252(13)/13^2 = 18/169 = 0.107, A081252(14)/14^2 = 20/196 = 0.102.

MATHEMATICA

CoefficientList[Series[-(x^2-x-1)/((x-1)*(x+1)*(2*x-1)), {x, 0, 33}], x] (* Vincenzo Librandi, Apr 04 2012 *)

PROG

(MAGMA) [Floor(2^n*5/3): n in [0..40]]; // Vincenzo Librandi, Apr 04 2012

CROSSREFS

Cf. A053646, A081252, A081253, A020714, A052549, A020989, A072197, A048573, A000975.

Sequence in context: A265385 A019300 A072762 * A125049 A267581 A164991

Adjacent sequences:  A081251 A081252 A081253 * A081255 A081256 A081257

KEYWORD

nonn

AUTHOR

Klaus Brockhaus, Mar 17 2003

STATUS

approved

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Last modified March 25 21:19 EDT 2017. Contains 284111 sequences.