A164537 a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 5, a(1) = 28.

5, 28, 154, 840, 4564, 24752, 134120, 726432, 3933776, 21300160, 115328416, 624425088, 3380802880, 18304471808, 99104534144, 536573667840, 2905125864704, 15728975567872, 85160042437120, 461074681546752

Offset: 0

Author

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

Keywords

• nonn
• easy

Comments

Binomial transform of A102285 without initial term 1. Fourth binomial transform of A164682. Inverse binomial transform of A164538.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..158
• Index entries for linear recurrences with constant coefficients, signature (8, -14).

Crossrefs

Cf. A102285, A164682, A164538.

Programs

Magma

Z:=PolynomialRing(Integers()); N:=NumberField(x^2-2); S:=[ ((5+4*r)*(4+r)^n+(5-4*r)*(4-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 21 2009

Formula

a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 5, a(1) = 28.

G.f.: (5-12*x)/(1-8*x+14*x^2).

a(n) = ((5+4*sqrt(2))*(4+sqrt(2))^n + (5-4*sqrt(2))*(4-sqrt(2))^n)/2.

Extensions

Edited and extended beyond a(5) by Klaus Brockhaus, Aug 21 2009