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A290996 p-INVERT of (1,1,1,1,1,...), where p(S) = 1 - S - S^4. 2
1, 2, 4, 9, 22, 55, 136, 330, 789, 1872, 4433, 10510, 24968, 59409, 141470, 336935, 802340, 1910166, 4546845, 10822176, 25758097, 61308650, 145928764, 347350473, 826795942, 1968018151, 4684451824, 11150316882, 26540849109, 63174538224, 150372815489 (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 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 (5, -9, 7, -1)

FORMULA

a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - a(n-4) for n >= 4.

G.f.: (1 - 3*x + 3*x^2) / (1 - 5*x + 9*x^2 - 7*x^3 + x^4). - Colin Barker, Aug 22 2017

MATHEMATICA

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

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

Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1]  (* A290996 *)

PROG

(PARI) Vec((1 - 3*x + 3*x^2) / (1 - 5*x + 9*x^2 - 7*x^3 + x^4) + O(x^50)) \\ Colin Barker, Aug 22 2017

CROSSREFS

Cf. A000012, A289780, A291000.

Sequence in context: A098719 A274289 A265023 * A198520 A115324 A196307

Adjacent sequences:  A290993 A290994 A290995 * A290997 A290998 A290999

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Aug 22 2017

STATUS

approved

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Last modified November 20 14:54 EST 2019. Contains 329337 sequences. (Running on oeis4.)