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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A247907 Expansion of (1 + x) / ((1 - x^4) * (1 - x - x^5)) in powers of x. 2
1, 2, 2, 2, 3, 5, 7, 9, 12, 16, 21, 28, 38, 51, 67, 88, 117, 156, 207, 274, 363, 481, 637, 844, 1119, 1483, 1964, 2601, 3446, 4566, 6049, 8013, 10615, 14062, 18628, 24677, 32691, 43307, 57369, 75997, 100675, 133367, 176674, 234043, 310041, 410717, 544084 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1,1,-1,1,-1).

FORMULA

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

a(n) = -A247918(-8-n) for all n in Z.

Convolution of A003520 and A133872.

0 = a(n) + a(n+4) - a(n+5) + mod(floor((n-1) / 2), 2) for all n in Z.

0 = a(n) - a(n+1) + a(n+2) - a(n+3) + a(n+4) - 2*a(n+5) + 2*a(n+6) - 2*a(n+7) + a(n+8) for all n in Z.

EXAMPLE

G.f. = 1 + 2*x + 2*x^2 + 2*x^3 + 3*x^4 + 5*x^5 + 7*x^6 + 9*x^7 + 12*x^8 + ...

MATHEMATICA

CoefficientList[Series[(1 + x)/((1 - x^4) (1 - x - x^5)), {x, 0, 100}], x] (* Vincenzo Librandi, Sep 27 2014 *)

PROG

(PARI) {a(n) = if( n<0, n=-8-n; polcoeff( -1 / ((1 - x) * (1 - x + x^2) * (1 + x^2) * (1 + x - x^3)) + x * O(x^n), n), polcoeff( 1 / ((1 - x) * (1 - x + x^2) * (1 + x^2) * (1 - x^2 - x^3)) + x * O(x^n), n))};

(MAGMA) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1 +x)/((1-x^4)*(1-x-x^5))));  // G. C. Greubel, Aug 04 2018

CROSSREFS

Cf. A003520, A133872, A247918.

Sequence in context: A320786 A126111 A296103 * A122789 A291294 A014208

Adjacent sequences:  A247904 A247905 A247906 * A247908 A247909 A247910

KEYWORD

nonn,easy

AUTHOR

Michael Somos, Sep 26 2014

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 24 13:17 EDT 2019. Contains 324325 sequences. (Running on oeis4.)