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A291010 p-INVERT of (1,1,1,1,1,...), where p(S) = (1 - 2 S)(1 - 3 S). 2
5, 24, 108, 468, 1980, 8244, 33948, 138708, 563580, 2280564, 9200988, 37040148, 148869180, 597602484, 2396787228, 9606280788, 38482518780, 154102262004, 616925608668, 2469252116628, 9881657512380, 39540577187124, 158204150161308, 632942124883668 (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 (7, -12)

FORMULA

G.f.: (5 - 11 x)/(1 - 7 x + 12 x^2).

a(n) = 7*a(n-1) - 12*a(n-2) for n >= 3.

a(n) = 9*4^n - 4*3^n. - Colin Barker, Aug 23 2017

MATHEMATICA

z = 60; s = x/(1 - x); p = (1 - 2 s) (1 - 3 s);

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

Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1]  (* A291010 *)

PROG

(PARI) Vec((5 - 11*x) / ((1 - 3*x)*(1 - 4*x)) + O(x^30)) \\ Colin Barker, Aug 23 2017

CROSSREFS

Cf. A000012, A289780, A291000.

Sequence in context: A271009 A270186 A008464 * A063001 A000953 A183934

Adjacent sequences:  A291007 A291008 A291009 * A291011 A291012 A291013

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Aug 23 2017

STATUS

approved

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Last modified August 1 03:48 EDT 2021. Contains 346380 sequences. (Running on oeis4.)