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A164604 a(n) = ((1+4*sqrt(2))*(3+2*sqrt(2))^n + (1-4*sqrt(2))*(3-2*sqrt(2))^n)/2. 3
1, 19, 113, 659, 3841, 22387, 130481, 760499, 4432513, 25834579, 150574961, 877615187, 5115116161, 29813081779, 173763374513, 1012767165299, 5902839617281, 34404270538387, 200522783613041, 1168732431139859 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A164603. Third binomial transform of A164702. Inverse binomial transform of A164605.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..155 from Vincenzo Librandi)

Index entries for linear recurrences with constant coefficients, signature (6,-1).

FORMULA

a(n) = 6*a(n-1) - a(n-2) for n > 1; a(0) = 1, a(1) = 19.

G.f.: (1+13*x)/(1-6*x+x^2).

E.g.f.: exp(3*x)*( cosh(2*sqrt(2)*x) + 4*sqrt(2)*sinh(2*sqrt(2)*x) ). - G. C. Greubel, Aug 11 2017

MATHEMATICA

LinearRecurrence[{6, -1}, [1, 19}, 50] (* G. C. Greubel, Aug 11 2017 *)

PROG

(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+4*r)*(3+2*r)^n+(1-4*r)*(3-2*r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 23 2009

(PARI) Vec((1+13*x)/(1-6*x+x^2)+O(x^99)) \\ Charles R Greathouse IV, Jun 12 2011

CROSSREFS

Cf. A164603, A164702, A164605.

Sequence in context: A080442 A033655 A245753 * A142370 A084751 A041694

Adjacent sequences:  A164601 A164602 A164603 * A164605 A164606 A164607

KEYWORD

nonn,easy

AUTHOR

Al Hakanson (hawkuu(AT)gmail.com), Aug 17 2009

EXTENSIONS

Edited and extended beyond a(5) by Klaus Brockhaus, Aug 23 2009

STATUS

approved

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Last modified January 22 15:57 EST 2019. Contains 319364 sequences. (Running on oeis4.)