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A291016 p-INVERT of (1,1,1,1,1,...), where p(S) = 1 - 4 S + S^2. 2
4, 19, 90, 426, 2016, 9540, 45144, 213624, 1010880, 4783536, 22635936, 107114400, 506870784, 2398538304, 11350005120, 53708800896, 254152774656, 1202663842560, 5691066407424, 26930415389184, 127436093890560, 603034071008256, 2853587862706176 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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 A291000 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 (6, -6)

FORMULA

G.f.: (4 - 5 x)/(1 - 6 x + 6 x^2).

a(n) = 6*a(n-1) - 6*a(n-2) n >= 3.

MATHEMATICA

z = 60; s = x/(1 - x); p = 1 - 4 s + s^2;

Drop[CoefficientList[Series[s, {x, 0, z}], x], 1]  (* A000012 *)

Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1]  (* A291016 *)

CROSSREFS

Cf. A000012, A289780, A291000.

Sequence in context: A015530 A256959 A181880 * A010907 A229242 A087449

Adjacent sequences:  A291013 A291014 A291015 * A291017 A291018 A291019

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Aug 23 2017

STATUS

approved

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Last modified May 16 08:07 EDT 2021. Contains 343940 sequences. (Running on oeis4.)