

A161947


a(n) = ((4+sqrt(2))*(5+sqrt(2))^n + (4sqrt(2))*(5sqrt(2))^n)/4.


2



2, 11, 64, 387, 2398, 15079, 95636, 609543, 3895802, 24938531, 159781864, 1024232427, 6567341398, 42116068159, 270111829436, 1732448726703, 11111915190002, 71272831185851, 457154262488464, 2932267507610067
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OFFSET

0,1


COMMENTS

Fifth binomial transform of A135530.


LINKS

Muniru A Asiru, Table of n, a(n) for n = 0..252
Index entries for linear recurrences with constant coefficients, signature (10,23).


FORMULA

a(n) = 10*a(n1)  23*a(n2) for n>1; a(0) = 2; a(1) = 11.
G.f.: (29*x)/(110*x+23*x^2).


MAPLE

seq(simplify(((4+sqrt(2))*(5+sqrt(2))^n+(4sqrt(2))*(5sqrt(2))^n)*1/4), n = 0 .. 20); # Emeric Deutsch, Jun 28 2009


MATHEMATICA

LinearRecurrence[{10, 23}, {2, 11}, 50] (* G. C. Greubel, Aug 17 2018 *)


PROG

(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^22); S:=[ ((4+r)*(5+r)^n+(4r)*(5r)^n)/4: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 01 2009
(GAP) a := [2, 11];; for n in [3..10^2] do a[n] := 10*a[n1]  23*a[n2]; od; a; # Muniru A Asiru, Feb 02 2018
(PARI) x='x+O('x^30); Vec((29*x)/(110*x+23*x^2)) \\ G. C. Greubel, Aug 17 2018


CROSSREFS

Cf. A135530.
Sequence in context: A126745 A179120 A038725 * A001565 A199412 A074613
Adjacent sequences: A161944 A161945 A161946 * A161948 A161949 A161950


KEYWORD

nonn


AUTHOR

Al Hakanson (hawkuu(AT)gmail.com), Jun 22 2009


EXTENSIONS

Edited and extended beyond a(4) by Klaus Brockhaus, Jul 01 2009
Extended by Emeric Deutsch, Jun 28 2009


STATUS

approved



