0,2

a(n) + A081342(n) = 8^n; e.g. a(4) + A081342(4) = 2040 + 2056 = 4096 = 8^4.

a(n) is a leg in a Pythagorean triangle along with A081342(n) (the hypotenuse) and 4^n. Example: a(4) = 2040, A081342(4) = 2056; then sqrt(2056^2 - 2040^2) = 256 = 4^4. Characteristic polynomial of M = x^2 -10x + 16.

Order of modular group of degree 2^(n-1)+1 - Artur Jasinski (grafix(AT)csl.pl), Aug 04 2007

E. Mathieu, Memoire sur la nombre de valeurs que peut acquirer une fonction quand on y permut ses variables de toutes les maniers possibles, Journ. de math. (2) 5 (1860), 9-42 (see p. 39).

Given M = 2 X 2 matrix [5,3; 3,5]; M^n * [1,0] = [A081342(a), a(n)]. E.g. a(4) = 2040, right term in = M^4 * [1,0] = [2056, 2040] = [A081342(4), a(4)].

a(n) = (2^(n-2))*(2^(2n-2)-1). - Artur Jasinski (grafix(AT)csl.pl), Aug 04 2007

a[0]:=0: a[1]:=3; for n from 2 to 20 do a[n]:=10*a[n-1]-16*a[n-2] end do: seq(a[n], n = 0 .. 20); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 16 2007

seq(binomial(2^n, 2)*(2^n + 1), n=0..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 07 2008

Table[2^(x - 2) (2^(2 x - 2) - 1), {x, 1, 15}] - Artur Jasinski (grafix(AT)csl.pl), Aug 04 2007

Cf. A081342.

Cf. A016131.

Sequence in context: A130546 A051133 A043030 this_sequence A136896 A121085 A144282

Adjacent sequences: A120686 A120687 A120688 this_sequence A120690 A120691 A120692

nonn,easy

Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 25 2006

Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion of Andrew Plewe, Jul 13 2007

More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 16 2007