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A289975 p-INVERT of the Fibonacci numbers (A000045, including 0), where p(S) = 1 - S - S^2. 5
0, 1, 1, 4, 7, 18, 37, 85, 183, 407, 888, 1956, 4284, 9409, 20630, 45270, 99289, 217819, 477776, 1048053, 2298912, 5042783, 11061455, 24263687, 53223023, 116746272, 256086074, 561731936, 1232174181, 2702807740, 5928681960, 13004724921, 28526216361 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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 A290890 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 (2, 2, -3, -1)

FORMULA

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

a(n) = 2*a(n-1) + 2*a(n-2) - 3*a(n-3) - a(n-4).

MATHEMATICA

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

Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A000045 *)

Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1]  (* A289975 *)

CROSSREFS

Cf. A000045, A289781, A289976, A289780.

Sequence in context: A146387 A219498 A219754 * A124400 A077920 A234269

Adjacent sequences:  A289972 A289973 A289974 * A289976 A289977 A289978

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Aug 21 2017

STATUS

approved

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Last modified March 24 01:20 EDT 2019. Contains 321444 sequences. (Running on oeis4.)