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A152261 a(n) = ((9 + sqrt(5))^n + (9 - sqrt(5))^n)/2. 1
1, 9, 86, 864, 9016, 96624, 1054016, 11628864, 129214336, 1442064384, 16136869376, 180866755584, 2029199527936, 22779718078464, 255815761289216, 2873425129242624, 32279654468386816, 362653470608523264 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A152109. - Philippe Deléham, Dec 03 2008

LINKS

Table of n, a(n) for n=0..17.

FORMULA

From Philippe Deléham, Dec 03 2008: (Start)

a(n) = 18*a(n-1) - 76*a(n-2), n > 1; a(0)=1, a(1)=9.

G.f.: (1-9*x)/(1-18*x+76*x^2).

a(n) = Sum_{k=0..n} A098158(n,k)*9^(2k-n)*5^(n-k). (End)

PROG

(MAGMA) Z<x>:= PolynomialRing(Integers()); N<r5>:=NumberField(x^2-5); S:=[ ((9+r5)^n+(9-r5)^n)/2: n in [0..17] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Dec 03 2008

CROSSREFS

Sequence in context: A204465 A276242 A015581 * A028339 A180751 A266828

Adjacent sequences:  A152258 A152259 A152260 * A152262 A152263 A152264

KEYWORD

nonn

AUTHOR

Al Hakanson (hawkuu(AT)gmail.com), Dec 01 2008

EXTENSIONS

Extended beyond a(6) by Klaus Brockhaus, Dec 03 2008

STATUS

approved

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Last modified October 16 15:31 EDT 2019. Contains 328101 sequences. (Running on oeis4.)