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

Author

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

Keywords

• nonn

Comments

Binomial transform is A152265, inverse binomial transform is A146966.

Links

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

Crossrefs

Cf. A098158, A152265, A146966.

Programs

Magma

Z:= PolynomialRing(Integers()); N:=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

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

Extensions

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

Edited by Klaus Brockhaus, Jul 09 2009