This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A291217 p-INVERT of (0,1,0,1,0,1,...), where p(S) = 1 - S^3. 2
 0, 0, 1, 0, 3, 1, 6, 6, 11, 21, 24, 57, 66, 138, 194, 330, 546, 827, 1452, 2175, 3739, 5826, 9582, 15519, 24807, 40836, 64933, 106584, 170796, 277696, 448980, 724968, 1177181, 1897380, 3080367, 4972113, 8055918, 13029534, 21075947, 34125561, 55169988 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 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 A291219 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 (0,3, 1,-3,0,1) FORMULA G.f.: -(x^2/((-1 + x + x^2) (1 + x - x^2 - x^3 + x^4))). a(n) = 3*a(n-2) + a(n-3) - 3*a(n-4) + a(n-6) for n >= 7. MATHEMATICA z = 60; s = x/(1 - x^2); p = 1 - s^3; Drop[CoefficientList[Series[s, {x, 0, z}], x], 1]  (* A000035 *) Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1]  (* A291217 *) LinearRecurrence[{0, 3, 1, -3, 0, 1}, {0, 0, 1, 0, 3, 1}, 50] (* Vincenzo Librandi, Aug 25 2017 *) PROG (MAGMA) I:=[0, 0, 1, 0, 3, 1]; [n le 6 select I[n] else 3*Self(n-2)+Self(n-3)-3*Self(n-4)+Self(n-6): n in [1..45]]; // Vincenzo Librandi, Aug 25 2017 CROSSREFS Cf. A000035, A291000, A291219. Sequence in context: A210744 A242729 A112692 * A198614 A239385 A124929 Adjacent sequences:  A291214 A291215 A291216 * A291218 A291219 A291220 KEYWORD nonn,easy AUTHOR Clark Kimberling, Aug 24 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 August 21 05:32 EDT 2019. Contains 326162 sequences. (Running on oeis4.)