The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A164608 Expansion of (1+4*x)/(1-8*x+8*x^2). 3
 1, 12, 88, 608, 4160, 28416, 194048, 1325056, 9048064, 61784064, 421888000, 2880831488, 19671547904, 134325731328, 917233467392, 6263261888512, 42768227368960, 292039723843584, 1994171971796992, 13617057983627264 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A054490. Fourth binomial transform of A164683. Inverse binomial transform of A164609. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..149 from Vincenzo Librandi) Index entries for linear recurrences with constant coefficients, signature (8,-8). FORMULA a(n) = 8*a(n-1) - 8*a(n-2) for n > 1; a(0) = 1, a(1) = 12. a(n) = A057084(n) + 4*A057084(n-1). a(n) = ((2+4*sqrt(2))*(4+2*sqrt(2))^n + (2-4*sqrt(2))*(4-2*sqrt(2))^n)/4. E.g.f.: exp(4*x)*(cosh(2*sqrt(2)*x) + 2*sqrt(2)*sinh(2*sqrt(2)*x)). - G. C. Greubel, Aug 10 2017 MAPLE a:=series((1+4*x)/(1-8*x+8*x^2), x=0, 20): seq(coeff(a, x, n), n=0..19); # Paolo P. Lava, Mar 28 2019 MATHEMATICA LinearRecurrence[{8, -8}, {1, 12, 88}, 50] (* G. C. Greubel, Aug 10 2017 *) PROG (MAGMA) Z:=PolynomialRing(Integers()); N:=NumberField(x^2-2); S:=[ ((2+4*r)*(4+2*r)^n+(2-4*r)*(4-2*r)^n)/4: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 22 2009 (PARI) x='x+O('x^50); Vec((1+4*x)/(1-8*x+8*x^2)) \\ G. C. Greubel, Aug 10 2017 CROSSREFS Cf. A054490, A164683, A164609. Sequence in context: A178257 A057406 A125349 * A081009 A155635 A126507 Adjacent sequences:  A164605 A164606 A164607 * A164609 A164610 A164611 KEYWORD nonn,easy AUTHOR Al Hakanson (hawkuu(AT)gmail.com), Aug 17 2009 EXTENSIONS Edited and extended beyond a(5) by Klaus Brockhaus, Aug 22 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 9 07:57 EDT 2021. Contains 343693 sequences. (Running on oeis4.)