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A161729
a(n) = ((4+sqrt(3))*(8+2*sqrt(3))^n-(4-sqrt(3))*(8-2*sqrt(3))^n)/(2*sqrt(3)).
3
1, 16, 204, 2432, 28304, 326400, 3750592, 43036672, 493555968, 5658988544, 64878906368, 743795097600, 8527018430464, 97754949812224, 1120674238611456, 12847530427547648, 147285426432966656, 1688495240694988800, 19357081676605554688, 221911554309549457408, 2544016621769302474752
OFFSET
0,2
COMMENTS
Eighth binomial transform of A162466.
FORMULA
a(n) = 16*a(n-1) - 52(n-2) for n > 1; a(0) = 1, a(1) = 16.
G.f.: 1/(1 - 16*x + 52*x^2). - Klaus Brockhaus, Jun 19 2009
a(n) = 2^n*A153594(n). - M. F. Hasler, Dec 03 2014
E.g.f.: exp(8*x)*(3*cosh(2*sqrt(3)*x) + 4*sqrt(3)*sinh(2*sqrt(3)*x))/3. - Stefano Spezia, Dec 31 2022
MATHEMATICA
Join[{a=1, b=16}, Table[c=16*b-52*a; a=b; b=c, {n, 40}]] (* Vladimir Joseph Stephan Orlovsky, Feb 08 2011 *)
LinearRecurrence[{16, -52}, {1, 16}, 20] (* Harvey P. Dale, Dec 23 2020 *)
PROG
(PARI) F=nfinit(x^2-3); for(n=0, 17, print1(nfeltdiv(F, ((4+x)*(8+2*x)^n-(4-x)*(8-2*x)^n), (2*x))[1], ", ")) \\ Klaus Brockhaus, Jun 19 2009
(PARI) Vec(1/(1-16*x+52*x^2)+O(x^25)) \\ M. F. Hasler, Dec 03 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jun 17 2009
EXTENSIONS
Extended beyond a(5) by Klaus Brockhaus, Jun 19 2009
Edited by Klaus Brockhaus, Jul 05 2009, and M. F. Hasler, Dec 03 2014
STATUS
approved