|
| |
|
|
A154245
|
|
a(n) = ((4+sqrt(7))^n-(4-sqrt(7))^n)/(2*sqrt(7)).
|
|
3
| |
|
|
1, 8, 55, 368, 2449, 16280, 108199, 719072, 4778785, 31758632, 211059991, 1402652240, 9321678001, 61949553848, 411701328775, 2736064645568, 18183205205569, 120841059834440, 803079631825399, 5337067516093232
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| Second binomial transform of A109115.
lim_{n -> infinity} a(n)/a(n-1) = 4+sqrt(7) = 6.6457513110....
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..100
Index to sequences with linear recurrences with constant coefficients, signature (8,-9).
|
|
|
FORMULA
| a(n) = 8*a(n-1)-9*a(n-2) for n>1; a(0)=0, a(1)=1. G.f.: x/(1-8*x+9*x^2). [From Philippe DELEHAM, Jan 06 2009]
a(n) = b such that 3^(n-1)/2*Integral_{x=0..Pi/2} (sin(n*x))/(4/3-cos(x)) dx = c+b*ln(2). [From Francesco Daddi, Aug 02 2011]
|
|
|
MATHEMATICA
| Join[{a=1, b=8}, Table[c=8*b-9*a; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 19 2011*)
|
|
|
PROG
| (MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-7); S:=[ ((4+r)^n-(4-r)^n)/(2*r): n in [1..20] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus, Jan 07 2009]
(Sage) [lucas_number1(n, 8, 9) for n in xrange(1, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
|
|
|
CROSSREFS
| Equals (A094432 without initial term 0)/3.
Cf. A010465 (decimal expansion of square root of 7), A109115.
Sequence in context: A026994 A110184 A013698 * A143420 A075734 A033890
Adjacent sequences: A154242 A154243 A154244 * A154246 A154247 A154248
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Al Hakanson (hawkuu(AT)gmail.com), Jan 05 2009
|
|
|
EXTENSIONS
| Extended beyond a(7) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 07 2009
Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 06 2009
|
| |
|
|
