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 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A291403 p-INVERT of (1,1,0,0,0,0,...), where p(S) = 1 - 2 S^2 - S^4. 2
 0, 2, 4, 7, 20, 42, 92, 214, 472, 1062, 2396, 5361, 12052, 27074, 60764, 136497, 306520, 688292, 1545768, 3471224, 7795184, 17505588, 39311608, 88280985, 198250312, 445204610, 999783508, 2245185343, 5041947516, 11322557726, 25426742788, 57100105470 (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 A291382 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, 2, 4, 3, 4, 6, 4, 1) FORMULA G.f.: -((x (1 + x)^2 (2 + x^2 + 2 x^3 + x^4))/(-1 + 2 x^2 + 4 x^3 + 3 x^4 + 4 x^5 + 6 x^6 + 4 x^7 + x^8)). a(n) = 2*a(n-2) + 4*a(n-3) + 3*a(n-4) + 4*a(n-5) + 6*a(n-6) + 4*a(n-7) + a(n-8) for n >= 9. MATHEMATICA z = 60; s = x + x^2; p = 1 - 2 s^2 - s^4; Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A019590 *) u = Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1] (* A291403 *) CROSSREFS Cf. A019590, A291382. Sequence in context: A243049 A247234 A327444 * A101805 A145777 A188497 Adjacent sequences: A291400 A291401 A291402 * A291404 A291405 A291406 KEYWORD nonn,easy AUTHOR Clark Kimberling, Sep 07 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 10 08:26 EST 2023. Contains 367701 sequences. (Running on oeis4.)