OFFSET
0,2
LINKS
Robert Israel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (12,-29).
FORMULA
a(n) = 12*a(n-1)-29*a(n-2), a(0)=1, a(1)=6. - Philippe Deléham, Nov 05 2008
G.f.: (1-6*x)/(1-12*x+29*x^2). - Klaus Brockhaus, Nov 05 2008
a(n) = (Sum_{k=0..n} A098158(n,k)*6^(2*k)*7^(n-k))/6^n. - Philippe Deléham, Nov 06 2008
E.g.f.: exp(6*x)*cosh(sqrt(7)*x). - G. C. Greubel, Jan 08 2020
EXAMPLE
a(3) = ((6 + sqrt(7))^3 + (6 - sqrt(7))^3) / 2 = 342.
MAPLE
f:= gfun:-rectoproc({a(n) = 12*a(n-1)-29*a(n-2), a(0)=1, a(1)=6}, a(n), remember):
map(f, [$0..100]); # Robert Israel, Feb 01 2016
MATHEMATICA
RecurrenceTable[{a[1]==1, a[2]==6, a[n]== 12 a[n-1] - 29 a[n-2]}, a, {n, 20}] (* Vincenzo Librandi, Jan 31 2016 *)
LinearRecurrence[{12, -29}, {1, 6}, 20] (* Harvey P. Dale, Apr 17 2018 *)
PROG
(Magma) Z<x>:= PolynomialRing(Integers()); N<r7>:=NumberField(x^2-7); S:=[ ((6+r7)^n+(6-r7)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 05 2008
(Magma) I:=[1, 6]; [n le 2 select I[n] else 12*Self(n-1)-29*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jan 31 2016
(PARI) Vec((1-6*x)/(1-12*x+29*x^2) + O(x^30)); \\ Michel Marcus, Jan 31 2016
(Sage)
def A146966_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1-6*x)/(1-12*x+29*x^2) ).list()
A146966_list(20) # G. C. Greubel, Jan 08 2020
(GAP) a:=[1, 6];; for n in [3..20] do a[n]:12*a[n-1]-29*a[n-2]; od; a; # G. C. Greubel, Jan 08 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Nov 03 2008
EXTENSIONS
Extended beyond a(7) by Klaus Brockhaus, Nov 05 2008
Typo in name corrected by Sean Reeves, Dec 19 2015
STATUS
approved