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A120689 a(n) = 10*a(n-1) - 16*a(n-2), n>0. 4
0, 3, 30, 252, 2040, 16368, 131040, 1048512, 8388480, 67108608, 536870400, 4294966272, 34359736320, 274877902848, 2199023247360, 17592186028032, 140737488322560, 1125899906777088, 9007199254609920, 72057594037665792 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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, Aug 04 2007

REFERENCES

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

LINKS

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (10,-16).

FORMULA

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, Aug 04 2007

G.f. 3*x / ( (8*x-1)*(2*x-1) ). a(n) = 3*A016131(n-1). - R. J. Mathar, Feb 16 2011

MAPLE

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, Aug 16 2007

seq(binomial(2^n, 2)*(2^n + 1), n=0..19); # Zerinvary Lajos, Jan 07 2008

MATHEMATICA

Table[2^(x - 2) (2^(2 x - 2) - 1), {x, 1, 15}] (* Artur Jasinski, Aug 04 2007 *)

CROSSREFS

Cf. A081342, A016131.

Sequence in context: A332426 A043030 A178015 * A180426 A246246 A136896

Adjacent sequences:  A120686 A120687 A120688 * A120690 A120691 A120692

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Jun 25 2006

EXTENSIONS

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jul 13 2007

More terms from Emeric Deutsch, Aug 16 2007

STATUS

approved

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Last modified October 15 21:38 EDT 2021. Contains 348034 sequences. (Running on oeis4.)