A164591 a(n) = ((4 + sqrt(18))*(4 + sqrt(8))^n + (4 - sqrt(18))*(4 - sqrt(8))^n)/8 .

1, 7, 48, 328, 2240, 15296, 104448, 713216, 4870144, 33255424, 227082240, 1550614528, 10588258304, 72301150208, 493703135232, 3371215880192, 23020101959680, 157191088635904, 1073367893409792, 7329414438191104, 50048372358250496

Offset: 0

Author

Al Hakanson (hawkuu(AT)gmail.com), Aug 17 2009

Keywords

• nonn
• easy

Comments

Binomial transform of A001109 without initial 0. Fourth binomial transform of A096886. Inverse binomial transform of A164592.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..100 from Vincenzo Librandi)
• Index entries for linear recurrences with constant coefficients, signature (8,-8).

Crossrefs

Cf. A001109, A096886, A164592.

Programs

Magma

Z:=PolynomialRing(Integers()); N:=NumberField(x^2-2); S:=[ ((4+3*r)*(4+2*r)^n+(4-3*r)*(4-2*r)^n)/8: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 24 2009

Mathematica

LinearRecurrence[{8,-8}, {1,7}, 50] (* G. C. Greubel, Aug 12 2017 *)

PARI

Vec((1-x)/(1-8*x+8*x^2)+O(x^99)) \\ Charles R Greathouse IV, Jul 16 2011

Formula

a(n) = 8*a(n-1) - 8*a(n-2) for n > 1; a(0) = 1, a(1) = 7.

G.f.: (1-x)/(1-8*x+8*x^2).

E.g.f.: (1/4)*exp(4*x)*(4*cosh(2*sqrt(2)*x) + 3*sqrt(2)*sinh(2*sqrt(2)*x)). - G. C. Greubel, Aug 12 2017

Extensions

Extended by Klaus Brockhaus and R. J. Mathar Aug 24 2009