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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A038391 Expansion of (x^3+2*x+1) / ((x-1)^4*(x^2+x+1)^2). 1
1, 4, 7, 13, 23, 33, 48, 69, 90, 118, 154, 190, 235, 290, 345, 411, 489, 567, 658, 763, 868, 988, 1124, 1260, 1413, 1584, 1755, 1945, 2155, 2365, 2596, 2849, 3102, 3378, 3678, 3978, 4303, 4654, 5005, 5383, 5789, 6195, 6630, 7095, 7560, 8056, 8584, 9112, 9673 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Old Name was: Bisection of A028289.

REFERENCES

B. N. Cyvin et al., Enumeration of conjugated hydrocarbons..., Structural Chem., 6 (1995), 85-88, equation (8).

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (2,-1,2,-4,2,-1,2,-1).

FORMULA

G.f.: (x^3+2*x+1) / ((x-1)^4*(x^2+x+1)^2). - Colin Barker, Aug 30 2013

From Wesley Ivan Hurt, May 07 2016: (Start)

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

a(n) = Sum_{i=1..n+1} (1+floor((n+i+1)/3)) * (1+floor((n-i+1)/3)). (End)

MATHEMATICA

CoefficientList[Series[(x^3 + 2 x + 1)/((x - 1)^4 (x^2 + x + 1)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 22 2013 *)

LinearRecurrence[{2, -1, 2, -4, 2, -1, 2, -1}, {1, 4, 7, 13, 23, 33, 48, 69}, 50] (* Harvey P. Dale, Sep 22 2015 *)

CROSSREFS

Cf. A028289.

Sequence in context: A316861 A298354 A139217 * A073832 A265160 A090854

Adjacent sequences:  A038388 A038389 A038390 * A038392 A038393 A038394

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Colin Barker, Aug 30 2013

Name changed by Wesley Ivan Hurt, May 07 2016

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 October 16 08:45 EDT 2019. Contains 328056 sequences. (Running on oeis4.)