login
A146962
a(n) = 10*a(n-1) - 19*a(n-2) with a(0)=1, a(1)=5.
2
1, 5, 31, 215, 1561, 11525, 85591, 636935, 4743121, 35329445, 263175151, 1960492055, 14604592681, 108796577765, 810478516711, 6037650189575, 44977410078241, 335058747180485, 2496016680318271, 18594050606753495
OFFSET
0,2
COMMENTS
Binomial transform of A143648.
Inverse binomial transform of A145301.
FORMULA
a(n) = ((5 + sqrt(6))^n + (5 - sqrt(6))^n)/2.
G.f.: (1-5*x)/(1-10*x+19*x^2). - Philippe Deléham and Klaus Brockhaus, Nov 05 2008
a(n) = (Sum_{k=0..n} A098158(n,k)*5^(2*k)*6^(n-k))/5^n. - Philippe Deléham, Nov 06 2008
E.g.f.: exp(5*x)*cosh(sqrt(6)*x). - G. C. Greubel, Jan 08 2020
MAPLE
seq(coeff(series((1-5*x)/(1-10*x+19*x^2), x, n+1), x, n), n = 0..30); # G. C. Greubel, Jan 08 2020
MATHEMATICA
LinearRecurrence[{10, -19}, {1, 5}, 30] (* Harvey P. Dale, Apr 27 2014 *)
CoefficientList[Series[(1-5x)/(1-10x+19x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Apr 28 2014 *)
PROG
(Magma) Z<x>:= PolynomialRing(Integers()); N<r6>:=NumberField(x^2-6); S:=[ ((5+r6)^n+(5-r6)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 05 2008
(PARI) my(x='x+O('x^30)); Vec((1-5*x)/(1-10*x+19*x^2)) \\ G. C. Greubel, Jan 08 2020
(Sage)
def A146962_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1-5*x)/(1-10*x+19*x^2) ).list()
A146962_list(30) # G. C. Greubel, Jan 08 2020
(GAP) a:=[1, 5];; for n in [3..30] do a[n]:=10*a[n-1]-19*a[n-2]; od; a; # G. C. Greubel, Jan 08 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Nov 03 2008
EXTENSIONS
Extended beyond a(7) by Klaus Brockhaus, Nov 05 2008
Edited by Klaus Brockhaus, Jul 15 2009
Name from Philippe Deléham and Klaus Brockhaus, Nov 05 2008
STATUS
approved