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

0,1

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).

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.

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=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

Crossrefs

Cf. A102285, A164682, A164538.

Sequence in context: A283516 A126699 A267828 * A015536 A271808 A005785

Adjacent sequences: A164534 A164535 A164536 * A164538 A164539 A164540

Keyword

nonn,easy

Author

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

Extensions

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

Status

approved