A164542 a(n) = 8*a(n-1) - 8*a(n-2) for n > 1; a(0) = 1, a(1) = 16.

1, 16, 120, 832, 5696, 38912, 265728, 1814528, 12390400, 84606976, 577732608, 3945005056, 26938179584, 183945396224, 1256057733120, 8576898695168, 58566727696384, 399918632009728, 2730815234506752, 18647172819976192

Offset: 0

Author

Al Hakanson (hawkuu(AT)gmail.com), Aug 15 2009

Keywords

• nonn
• easy

Comments

Binomial transform of A164541. Fourth binomial transform of A164675. Inverse binomial transform of A164543.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..149
• Index entries for linear recurrences with constant coefficients, signature (8,-8).

Crossrefs

Cf. A164541, A164675, A164543.

Programs

Magma

Z:=PolynomialRing(Integers()); N:=NumberField(x^2-2); S:=[ ((1+3*r)*(4+2*r)^n+(1-3*r)*(4-2*r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 20 2009

Mathematica

LinearRecurrence[{8,-8},{1,16},30] (* Harvey P. Dale, Jul 23 2018 *)

Formula

a(n) = 8*a(n-1) - 8*a(n-2) for n > 1; a(0) = 1, a(1) = 16.

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

a(n) = ((1+3*sqrt(2))*(4+2*sqrt(2))^n + (1-3*sqrt(2))*(4-2*sqrt(2))^n)/2.

Extensions

Edited and extended beyond a(5) by Klaus Brockhaus, Aug 20 2009