The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A247281 4^n -(-1)^n. 5
 0, 5, 15, 65, 255, 1025, 4095, 16385, 65535, 262145, 1048575, 4194305, 16777215, 67108865, 268435455, 1073741825, 4294967295, 17179869185, 68719476735, 274877906945, 1099511627775, 4398046511105, 17592186044415 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Numerators of the first and second upper diagonals of the array 0, 0, 0, 5/4, 5/2, 75/16, 125/16,... = b(n)/c(n) 0, 0, 5/4, 5/4, 35/16, 25/8, 325/64,... 0, 5/4, 0, 15/16, 15/16, 125/64, 190/64,... 5/4, -5/4, 15/16, 0, 65/64, 65/64, 515/256,... -5/2, 35/16, -15/16, 65/64, 0, 255/256, 255/256,... etc. The denominators of the first row are c(n) = 1 followed by A084623(n). The inverse binomial transform of b(n)/c(n) is (-1)^(n+1)*b(n)/c(n). The main diagonal is 0's=A000004. These two characteristics of the difference array show that the first row is an autosequence of the first kind. a(n) mod 9 is a sequence of period 6: repeat 0, 5, 6, 2, 3, 8. LINKS Index entries for linear recurrences with constant coefficients, signature (3,4). OEIS Wiki, Autosequence FORMULA a(n) = 5*A015521(n). a(n+1) = 10*A037481(n) +5. a(n+1) = 4*a(n) + 5*(-1)^n. a(n) = 3*a(n-1) + 4*a(n-2). - Colin Barker, Sep 11 2014 G.f.: -5*x / ((x+1)*(4*x-1)). - Colin Barker, Sep 11 2014 MATHEMATICA LinearRecurrence[{3, 4}, {0, 5}, 23] (* Jean-François Alcover, May 22 2016 *) PROG (PARI) concat(0, Vec(-5*x / ((x+1)*(4*x-1)) + O(x^100))) \\ Colin Barker, Sep 11 2014 (PARI) vector(100, n, 4^(n-1)+(-1)^n) \\ Derek Orr, Sep 11 2014 CROSSREFS Cf. A000351, A015521, A037481, A084623. Sequence in context: A149620 A149621 A149622 * A149623 A149624 A149625 Adjacent sequences: A247278 A247279 A247280 * A247282 A247283 A247284 KEYWORD nonn,easy AUTHOR Paul Curtz, Sep 11 2014 EXTENSIONS Typos in data fixed by Colin Barker, Sep 11 2014 STATUS approved

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

Last modified December 5 19:04 EST 2022. Contains 358588 sequences. (Running on oeis4.)