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A292484 p-INVERT of the odd positive integers, where p(S) = 1 + S - S^2. 1
-1, -1, 4, 9, 5, 8, 63, 183, 348, 745, 2061, 5456, 12991, 30831, 76660, 192137, 472597, 1155032, 2843007, 7024935, 17315404, 42592489, 104847389, 258355104, 636507775, 1567442143, 3859933668, 9507231753, 23417547813, 57675809960, 142047927231, 349856144791 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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 A292480 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 (3, -4, 7, -1)

FORMULA

G.f.: ((1 + x) (-1 + 3 x))/(1 - 3 x + 4 x^2 - 7 x^3 + x^4).

a(n) = 3*a(n-1) - 4*a(n-2) + 7*a(n-3) - a(n-4)  for n >= 5.

MATHEMATICA

z = 60; s = x (x + 1)/(1 - x)^2; p = 1 + s - s^2;

Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A005408 *)

Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1]  (* A292484 *)

CROSSREFS

Cf. A005408, A292480.

Sequence in context: A200241 A243710 A242610 * A197418 A137807 A163103

Adjacent sequences:  A292481 A292482 A292483 * A292485 A292486 A292487

KEYWORD

easy,sign

AUTHOR

Clark Kimberling, Oct 02 2017

STATUS

approved

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Last modified November 12 17:06 EST 2019. Contains 329058 sequences. (Running on oeis4.)