|
| |
|
|
A154235
|
|
a(n) = ((4+sqrt(6))^n-(4-sqrt(6))^n)/(2*sqrt(6)).
|
|
4
| |
|
|
1, 8, 54, 352, 2276, 14688, 94744, 611072, 3941136, 25418368, 163935584, 1057300992, 6819052096, 43979406848, 283644733824, 1829363802112, 11798463078656, 76094066608128, 490767902078464, 3165202550546432
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| lim_{n -> infinity} a(n)/a(n-1) = 4+sqrt(6) = 6.4494897427....
Binomial transform of A164550, second binomial transform of A164549, third binomial transform of A123011, fourth binomial transform of A164532.
Binomial transform is A164551, second binomial transform is A164552, third binomial transform is A164553.
|
|
|
LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (8,-10).
|
|
|
FORMULA
| a(n) = 8*a(n-1)-10*a(n-2) for n>1; a(0)=0, a(1)=1. G.f.: x/(1-8x+10x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 06 2009]
|
|
|
MATHEMATICA
| Join[{a=1, b=8}, Table[c=8*b-10*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^2-6); S:=[ ((4+r)^n-(4-r)^n)/(2*r): n in [1..20] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 07 2009]
(Other) Sage: [lucas_number1(n, 8, 10) for n in xrange(1, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
|
|
|
CROSSREFS
| Cf. A010464 (decimal expansion of square root of 6), A123011, A164532, A164549, A164550, A164551, A164552, A164553.
Sequence in context: A091433 A081899 A057970 * A201640 A002775 A079754
Adjacent sequences: A154232 A154233 A154234 * A154236 A154237 A154238
|
|
|
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 04 2009
|
| |
|
|
