A145302 a(n) = ((7 + sqrt(7))^n + (7 - sqrt(7))^n)/2.

1, 7, 56, 490, 4508, 42532, 406112, 3899224, 37532432, 361686640, 3487250816, 33630672544, 324364881344, 3128620091968, 30177356271104, 291080943932800, 2807684251672832, 27082179878242048, 261227779725129728

Offset

0,2

Comments

Binomial transform is A152265, inverse binomial transform is A146966.

Links

Table of n, a(n) for n=0..18.

Index entries for linear recurrences with constant coefficients, signature (14, -42).

Formula

From R. J. Mathar, Oct 10 2008: (Start)

a(n) = 14*a(n-1) - 42*a(n-2).

G.f.: (1-7x)/(1-14x+42x^2). (End)

a(n) = Sum_{k=0..n} 7^k*A098158(n,k). - Philippe Deléham, Oct 14 2008

Prog

(Magma) Z<x>:= PolynomialRing(Integers()); N<r7>:=NumberField(x^2-7); S:=[ ((7+r7)^n+(7-r7)^n)/2: n in [0..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Oct 20 2008, Jul 09 2009

Crossrefs

Cf. A098158, A152265, A146966.

Sequence in context: A264912 A323216 A024091 * A233669 A265233 A165322

Adjacent sequences: A145299 A145300 A145301 * A145303 A145304 A145305

Keyword

nonn

Author

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

Extensions

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

Edited by Klaus Brockhaus, Jul 09 2009

Status

approved