A081253 Numbers k such that A081252(m)/m^2 has a local minimum for m = k.

2, 4, 9, 18, 37, 74, 149, 298, 597, 1194, 2389, 4778, 9557, 19114, 38229, 76458, 152917, 305834, 611669, 1223338, 2446677, 4893354, 9786709, 19573418, 39146837, 78293674, 156587349, 313174698, 626349397, 1252698794, 2505397589

Offset: 1

Author

Klaus Brockhaus, Mar 17 2003

Keywords

• nonn
• easy

Comments

The limit of the local minima, lim_{n->infinity} A081252(n)/n^2 = 1/14. For local maxima cf. A081254.

Examples

			9 is a term since A081252(8)/8^2 = 5/64 = 0.078, A081252(9)/9^2 = 6/81 = 0.074, A081252(10)/10^2 = 8/100 = 0.080.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..3321
• Klaus Brockhaus, Illustration for A053646, A081252, A081253 and A081254
• Chris J. Mitchell and Peter R. Wild, Constructing orientable sequences, arXiv:2108.03069 [math.CO], 2021. See Table 2 p. 12 but with different offset.
• Index entries for linear recurrences with constant coefficients, signature (2,1,-2).

Crossrefs

Cf. A053646, A081252, A081254, A005009, A062092.

Cf. A266071 (binary).

Programs

Mathematica

Rest@ CoefficientList[Series[-x (x^2 - 2)/((x - 1) (x + 1) (2 x - 1)), {x, 0, 31}], x]

Python

print([7*2**n//6 for n in range(1, 50)]) # Karl V. Keller, Jr., May 22 2022

Formula

a(n) = floor(2^(n-1)*7/3).

a(n) = a(n-2) + 7*2^(n-3) for n > 2; a(n+2) - a(n) = A005009(n-1); a(n+1) - a(n) = A062092(n-1).

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

a(n) = 2*a(n-1) for even n, otherwise a(n) = 2*a(n-1)+1, with a(1)=2. - Bruno Berselli, Jun 19 2014

Extensions

Formulas adjusted to be consistent with offset 1 by Pontus von Brömssen, Sep 27 2021