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A147688 a(n) = ((6 + sqrt(8))^n + (6 - sqrt(8))^n))/2. 0
1, 6, 44, 360, 3088, 26976, 237248, 2091648, 18456832, 162915840, 1438198784, 12696741888, 112091336704, 989587267584, 8736489783296, 77129433907200, 680931492954112, 6011553766047744, 53072563389857792, 468547255228956672 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (12, -28).

FORMULA

From Philippe Deléham, Nov 13 2008: (Start)

a(n) = 12*a(n-1) - 28*a(n-2), a(0)=1, a(1)=6.

G.f.: (1-6x)/(1-12x+28x^2).

a(n) = (Sum_{k=0..n} A098158(n,k)*6^(2k)*8^(n-k))/6^n.

MATHEMATICA

LinearRecurrence[{12, -28}, {1, 6}, 30]  (* Harvey P. Dale, Apr 23 2011 *)

PROG

(MAGMA) Z<x>:= PolynomialRing(Integers()); N<r8>:=NumberField(x^2-8); S:=[ ((6+r8)^n+(6-r8)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 13 2008

CROSSREFS

Sequence in context: A108452 A005591 A052204 * A090442 A286867 A084965

Adjacent sequences:  A147685 A147686 A147687 * A147689 A147690 A147691

KEYWORD

nonn,easy

AUTHOR

Al Hakanson (hawkuu(AT)gmail.com), Nov 10 2008

EXTENSIONS

Extended beyond a(6) by Klaus Brockhaus, Nov 13 2008

STATUS

approved

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Last modified March 19 13:08 EDT 2019. Contains 321330 sequences. (Running on oeis4.)