login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A291247 p-INVERT of (0,1,0,1,0,1,...), where p(S) = 1 - S - S^2 - S^3 + S^4. 2
1, 2, 5, 10, 24, 49, 112, 238, 526, 1142, 2491, 5442, 11842, 25873, 56344, 122975, 268042, 584633, 1274820, 2779895, 6062306, 13219186, 28827703, 62861754, 137082358, 298927682, 651861824, 1421488867, 3099781932, 6759580078, 14740333285, 32143687954 (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, -9, 2, 5, -1, -1)

FORMULA

G.f.: (1 + x - 2 x^2 - 3 x^3 + 2 x^4 + x^5 - x^6)/(1 - x - 5 x^2 + 2 x^3 + 9 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) - 9*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]  (* A291247 *)

CROSSREFS

Cf. A000035, A291219.

Sequence in context: A299436 A049937 A026754 * A316697 A032170 A084081

Adjacent sequences:  A291244 A291245 A291246 * A291248 A291249 A291250

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Aug 29 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 June 18 15:25 EDT 2019. Contains 324213 sequences. (Running on oeis4.)