A164537 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

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