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A146963 a(n) = ((3 + sqrt(7))^n + (3 - sqrt(7))^n)/2. 4
1, 3, 16, 90, 508, 2868, 16192, 91416, 516112, 2913840, 16450816, 92877216, 524361664, 2960415552, 16713769984, 94361788800, 532743192832, 3007735579392, 16980927090688, 95870091385344, 541258694130688 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A108851. Inverse binomial transform of A146964.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..158

FORMULA

From Philippe Deléham and Klaus Brockhaus, Nov 05 2008: (Start)

a(n) = 6*a(n-1) - 2*a(n-2); a(0)=1, a(1)=3.

G.f.: (1-3*x)/(1-6*x+2*x^2). (End)

a(n) = (Sum_{k=0..n} A098158(n,k)*3^(2*k)*7^(n-k))/3^n. - Philippe Deléham, Nov 06 2008

MATHEMATICA

Transpose[NestList[Join[{Last[#], 6Last[#]-2First[#]}]&, {1, 3}, 25]] [[1]]  (* or *) CoefficientList[Series[(1-3x)/(1-6x+2x^2), {x, 0, 25}], x]  (* Harvey P. Dale, Apr 11 2011 *)

PROG

(MAGMA) Z<x>:= PolynomialRing(Integers()); N<r7>:=NumberField(x^2-7); S:=[ ((3+r7)^n+(3-r7)^n)/2: n in [0..20] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 05 2008

CROSSREFS

Cf. A108851, A146964, A098158.

Sequence in context: A151329 A026111 A026330 * A074562 A130744 A009124

Adjacent sequences:  A146960 A146961 A146962 * A146964 A146965 A146966

KEYWORD

nonn

AUTHOR

Al Hakanson (hawkuu(AT)gmail.com), Nov 03 2008

EXTENSIONS

Extended beyond a(7) by Klaus Brockhaus, Nov 05 2008

Edited by Klaus Brockhaus, Jul 16 2009

STATUS

approved

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Last modified May 21 01:18 EDT 2019. Contains 323429 sequences. (Running on oeis4.)