This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A290911 p-INVERT of the positive integers, where p(S) = 1 - 6*S^2. 3
 0, 6, 24, 96, 408, 1722, 7248, 30528, 128592, 541638, 2281416, 9609504, 40475976, 170487930, 718108320, 3024727680, 12740386464, 53663491206, 226034767224, 952075887072, 4010217126648, 16891344084282, 71147645118192, 299679373092288, 1262272651579632 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Suppose s = (c(0), c(1), c(2), ...) is a sequence and p(S) is a polynomial. Let S(x) = c(0)*x + c(1)*x^2 + c(2)*x^3 + ... and T(x) = (-p(0) + 1/p(S(x)))/x. The p-INVERT of s is the sequence t(s) of coefficients in the Maclaurin series for T(x). Taking p(S) = 1 - S gives the "INVERT" transform of s, so that p-INVERT is a generalization of the "INVERT" transform (e.g., A033453). See A290890 for a guide to related sequences. LINKS Clark Kimberling, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (4, 0, 4, -1) FORMULA G.f.: (6 x)/(1 - 4 x - 4 x^3 + x^4). a(n) = 4*a(n-1) + 4*a(n-3) - a(n-4). a(n) = 6*A290912(n) for n >= 0. MATHEMATICA z = 60; s = x/(1 - x)^2; p = 1 - 6 s^2; Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A000027 *) u = Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1] (* A290911 *) u/6 (* A290912 *) CROSSREFS Cf. A000027, A290890, A290912. Sequence in context: A169759 A164908 A002023 * A037505 A048179 A117614 Adjacent sequences:  A290908 A290909 A290910 * A290912 A290913 A290914 KEYWORD nonn,easy AUTHOR Clark Kimberling, Aug 18 2017 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 December 18 19:04 EST 2018. Contains 318243 sequences. (Running on oeis4.)