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A147957 a(n) = ((6 + sqrt(2))^n + (6 - sqrt(2))^n)/2. 3
1, 6, 38, 252, 1732, 12216, 87704, 637104, 4663312, 34298208, 253025888, 1870171584, 13839178816, 102484311936, 759279663488, 5626889356032, 41707163713792, 309171726460416, 2292017151256064, 16992367115418624 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

6th binomial transform of A077957. Binomial transform of A083880. Inverse binomial transform of A147958. - Philippe Deléham, Nov 30 2008

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (12, -34).

FORMULA

From Philippe Deléham, Nov 19 2008: (Start)

a(n) = 12*a(n-1) - 34*a(n-2), n > 1; a(0)=1, a(1)=6.

G.f.: (1 - 6*x)/(1 - 12*x + 34*x^2).

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

E.g.f.: exp(6*x)*cosh(sqrt(2)*x). - Ilya Gutkovskiy, Aug 11 2017

MATHEMATICA

LinearRecurrence[{12, -34}, {1, 6}, 50] (* G. C. Greubel, Aug 17 2018 *)

PROG

(MAGMA) Z<x>:= PolynomialRing(Integers()); N<r2>:=NumberField(x^2-2); S:=[ ((6+r2)^n+(6-r2)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 19 2008

(PARI) x='x+O('x^50); Vec((1-6*x)/(1-12*x+34*x^2)) \\ G. C. Greubel, Aug 17 2018

CROSSREFS

Sequence in context: A217633 A162558 A215466 * A098410 A079949 A026940

Adjacent sequences:  A147954 A147955 A147956 * A147958 A147959 A147960

KEYWORD

nonn

AUTHOR

Al Hakanson (hawkuu(AT)blogspot.com), Nov 17 2008

EXTENSIONS

Extended beyond a(6) by Klaus Brockhaus, Nov 19 2008

STATUS

approved

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Last modified March 23 04:46 EDT 2019. Contains 321422 sequences. (Running on oeis4.)