A145301 a(n) = 12*a(n-1) - 30*a(n-2) with a(0)=1 and a(1)=6.

1, 6, 42, 324, 2628, 21816, 182952, 1540944, 13002768, 109804896, 927575712, 7836761664, 66213868608, 559463573376, 4727146822272, 39941854665984, 337487851323648, 2851598575904256, 24094547371141632, 203586611176571904, 1720202912984613888

Offset: 0

Author

Al Hakanson (hawkuu(AT)gmail.com), Oct 06 2008

Keywords

• nonn

Comments

Binomial transform is A152262, inverse binomial transform is A146962.

Links

• Index entries for linear recurrences with constant coefficients, signature (12, -30).

Crossrefs

Cf. A098158, A152262, A146962.

Programs

Magma

Z:= PolynomialRing(Integers()); N:=NumberField(x^2-6); S:=[ ((6+r6)^n+(6-r6)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Oct 20 2008

Mathematica

CoefficientList[Series[(1 - 6 x)/(1 - 12 x + 30 x^2), {x, 0, 20}], x] (* Wesley Ivan Hurt, Jun 14 2014 *)

Formula

G.f.: (1-6x)/(1-12x+30x^2). - R. J. Mathar, Oct 10 2008

a(n) = ((6+sqrt(6))^n+(6-sqrt(6))^n)/2.

a(n) = sum_{k, 0<=k<=n} 6^k * A098158(n,k). - Philippe Deléham, Oct 14 2008

Extensions

More terms from R. J. Mathar, Oct 10 2008

Corrected definition. - Philippe Deléham, Oct 15 2008

Edited by Klaus Brockhaus, Jul 08 2009