|
|
A152109
|
|
a(n) = ((8+sqrt(5))^n + (8-sqrt(5))^n)/2.
|
|
1
|
|
|
1, 8, 69, 632, 6041, 59368, 593469, 5992792, 60870001, 620345288, 6334194549, 64746740792, 662230374281, 6775628281768, 69338460425709, 709653298187032, 7263483605875681, 74346193100976008, 760993556868950949
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 16*a(n-1) - 59*a(n-2), n > 1; a(0)=1, a(1)=8.
G.f.: (1-8*x)/(1-16*x+59*x^2).
a(n) = (Sum_{k=0..n} A098158(n,k)*8^(2*k)*5^(n-k))/8^n. (End)
|
|
MATHEMATICA
|
LinearRecurrence[{16, -59}, {1, 8}, 30] (* Harvey P. Dale, Dec 18 2011 *)
|
|
PROG
|
(Magma) Z<x>:= PolynomialRing(Integers()); N<r5>:=NumberField(x^2-5); S:=[ ((8+r5)^n+(8-r5)^n)/2: n in [0..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 26 2008
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Al Hakanson (hawkuu(AT)gmail.com), Nov 24 2008
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|