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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A008679 Expansion of 1/((1-x^3)*(1-x^4)). 7
1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 4, 3, 4, 4, 4, 4, 4, 4, 5, 4, 4, 5, 5, 4, 5, 5, 5, 5, 5, 5, 6, 5, 5, 6, 6, 5, 6, 6, 6, 6, 6, 6, 7, 6, 6, 7, 7, 6, 7, 7, 7, 7, 7, 7, 8, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,13

COMMENTS

Number of partitions of n into parts 3 and 4. - Reinhard Zumkeller, Feb 09 2009

Convolution of A112689 (shifted left once) by A033999. - R. J. Mathar, Feb 13 2009

With four 0's prepended and offset 0, a(n) is the number of partitions of n into four parts whose largest three parts are equal. - Wesley Ivan Hurt, Jan 06 2021

LINKS

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 216

Index entries for linear recurrences with constant coefficients, signature (0,0,1,1,0,0,-1).

FORMULA

a(n+12) = a(n) + 1. - Reinhard Zumkeller, Feb 09 2009

G.f.: 1/((1-x)^2*(1+x)*(1+x+x^2)*(1+x^2)). - R. J. Mathar, Feb 13 2009

a(n) = 1 + floor(n/3) + floor(-n/4). - Tani Akinari, Sep 02 2013

E.g.f.: (1/72)*(9*exp(-x)+21*exp(x)+6*exp(x)*x+18*cos(x)+24*exp(-x/2)*cos(sqrt(3)*x/2)-18*sin(x)+8*sqrt(3)*exp(-x/2)*sin(sqrt(3)*x/2)). - Stefano Spezia, Sep 09 2019

a(n) = A005044(n+3) - A005044(n+1). - Yuchun Ji, Oct 10 2020

From Wesley Ivan Hurt, Jan 17 2021: (Start)

a(n) = a(n-3) + a(n-4) - a(n-7).

a(n) = Sum_{k=1..floor((n+4)/4)} Sum_{j=k..floor((n+4-k)/3)} Sum_{i=j..floor((n+4-j-k)/2)} [j = i = n+4-i-k-j], where [ ] is the Iverson bracket. (End)

MAPLE

seq(coeff(series(1/((1-x^3)*(1-x^4)), x, n+1), x, n), n = 0..90); # G. C. Greubel, Sep 09 2019

MATHEMATICA

LinearRecurrence[{0, 0, 1, 1, 0, 0, -1}, {1, 0, 0, 1, 1, 0, 1}, 90] (* Vladimir Joseph Stephan Orlovsky, Feb 23 2012 *)

CoefficientList[Series[1/((1-x)^2(1+x)(1+x+x^2)(1+x^2)), {x, 0, 90}], x] (* Vincenzo Librandi, Jun 11 2013 *)

PROG

(PARI) my(x='x+O('x^90)); Vec(1/((1-x^3)*(1-x^4))) \\ G. C. Greubel, Sep 09 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 90); Coefficients(R!( 1/((1-x^3)*(1-x^4)) )); // G. C. Greubel, Sep 09 2019

(Sage)

def A008679_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P(1/((1-x^3)*(1-x^4))).list()

A008679_list(90) # G. C. Greubel, Sep 09 2019

(GAP) a:=[1, 0, 0, 1, 1, 0, 1, 1];; for n in [8..90] do a[n]:=a[n-3]+a[n-4]-a[n-7]; od; a; # G. C. Greubel, Sep 09 2019

CROSSREFS

Cf. A005044, A033999, A112689.

Sequence in context: A196062 A283682 A087974 * A029435 A089643 A185090

Adjacent sequences:  A008676 A008677 A008678 * A008680 A008681 A008682

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

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 December 1 05:33 EST 2021. Contains 349426 sequences. (Running on oeis4.)