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A162561 a(n) = ((4+sqrt(3))*(5+sqrt(3))^nv+v(4-sqrt(3))*(5-sqrt(3))^n)/2. 2
4, 23, 142, 914, 6016, 40052, 268168, 1800536, 12105664, 81444848, 548123872, 3689452064, 24835795456, 167190009152, 1125512591488, 7576945713536, 51008180122624, 343388995528448, 2311709992586752, 15562542024241664 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Third binomial transform of A077236. Fourth binomial transform of A162559. Fifth binomial transform of A162766.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (10, -22).

FORMULA

a(n) = 10*a(n-1) - 22*a(n-2) for n > 2; a(0) = 4, a(1) = 23.

G.f.: (4-17*x)/(1-10*x+22*x^2).

MATHEMATICA

LinearRecurrence[{10, -22}, {4, 23}, 30] (* Harvey P. Dale, Mar 27 2013 *)

PROG

(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((4+r)*(5+r)^n+(4-r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 14 2009

CROSSREFS

Cf. A077236, A162559, A162766.

Sequence in context: A158197 A038736 A091642 * A277921 A020079 A146964

Adjacent sequences:  A162558 A162559 A162560 * A162562 A162563 A162564

KEYWORD

nonn

AUTHOR

Al Hakanson (hawkuu(AT)gmail.com), Jul 06 2009

EXTENSIONS

Edited and extended beyond a(5) by Klaus Brockhaus, Jul 14 2009

STATUS

approved

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Last modified March 22 01:06 EDT 2019. Contains 321406 sequences. (Running on oeis4.)