login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A290926 p-INVERT of the positive integers, where p(S) = (1 - S^2)^2. 2
0, 2, 8, 23, 64, 182, 520, 1475, 4152, 11624, 32408, 90028, 249272, 688140, 1894600, 5203665, 14260968, 39004962, 106486512, 290226621, 789776888, 2146082610, 5823823120, 15784464728, 42731452816, 115556460982, 312175750152, 842537682283, 2271900155120 (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 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 (8, -26, 48, -59, 48, -26, 8, -1)

FORMULA

G.f.: (2 x - 8 x^2 + 11 x^3 - 8 x^4 + 2 x^5)/(1 - 4 x + 5 x^2 - 4 x^3 + x^4)^2.

a(n) = 8*a(n-1) - 26*a(n-2) + 48*a(n-3) - 59*a(n-4) + 48*a(n-5) - 26*a(n-6) + 8*a(n-7) - a(n-8).

MATHEMATICA

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

Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A000027 *)

u = Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1]  (* A290926 *)

CROSSREFS

Cf. A000027, A290890.

Sequence in context: A255942 A180664 A294959 * A018042 A304304 A072842

Adjacent sequences:  A290923 A290924 A290925 * A290927 A290928 A290929

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Aug 19 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 9 04:17 EDT 2021. Contains 343685 sequences. (Running on oeis4.)