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A291234 p-INVERT of (0,1,0,1,0,1,...), where p(S) = 1 - S - S^2 - S^3 - S^4. 2
1, 2, 5, 12, 28, 67, 156, 370, 866, 2044, 4799, 11304, 26574, 62547, 147108, 346149, 814270, 1915795, 4506952, 10603417, 24945414, 58687660, 138068915, 324824928, 764187814, 1797846170, 4229645000, 9950753025, 23410332344, 55075627972, 129572006209 (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 A291219 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 (1, 5, -2, -7, 2, 5, -1, -1)

FORMULA

G.f.: (1 + x - 2 x^2 - x^3 + 2 x^4 + x^5 - x^6)/(1 - x - 5 x^2 + 2 x^3 + 7 x^4 - 2 x^5 - 5 x^6 + x^7 + x^8).

a(n) = a(n-1) + 5*a(n-2) - 2*a(n-3) - 7*a(n-4) + 2*a(n-5) + 5*a(n-6) - a(n-7) - a(n-8) for n >= 9.

MATHEMATICA

z = 60; s = x/(1 - x^2); p = 1 - s - s^2 - s^3 - s^4;

Drop[CoefficientList[Series[s, {x, 0, z}], x], 1]  (* A000035 *)

Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1]  (* A291234 *)

CROSSREFS

Cf. A000035, A291219.

Sequence in context: A255115 A166297 A024960 * A238828 A162036 A321253

Adjacent sequences:  A291231 A291232 A291233 * A291235 A291236 A291237

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Aug 26 2017

STATUS

approved

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Last modified June 18 07:06 EDT 2019. Contains 324203 sequences. (Running on oeis4.)