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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A160050 Numerator of the Harary number for the star graph s_n. 12
0, 1, 5, 9, 7, 10, 27, 35, 22, 27, 65, 77, 45, 52, 119, 135, 76, 85, 189, 209, 115, 126, 275, 299, 162, 175, 377, 405, 217, 232, 495, 527, 280, 297, 629, 665, 351, 370, 779, 819, 430, 451, 945, 989, 517, 540, 1127, 1175, 612, 637, 1325, 1377, 715, 742, 1539 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

Eric Weisstein's World of Mathematics, Harary Index

Index entries for linear recurrences with constant coefficients, signature (3,-6,10,-12,12,-10,6,-3,1).

FORMULA

Numerator of (1/4)*(n+2)*(n-1). - Joerg Arndt, Jan 04 2011

It appears that a(n + 1) = A060819(n-1) * A060819(n + 2). - Paul Curtz, Dec 23 2010 [Corrected by Joerg Arndt, Jan 04 2011]

G.f.:  x^2*(-1-2*x-5*x^4+3*x^5-2*x^6+x^7) / ( (x-1)^3*(x^2+1)^3 ). - R. J. Mathar, Jan 04 2011

a(1+4*n) = (A000217(n+1)-1)/2, a(2+4*n) = (A000217(n+2)-1)/2, a(3+4*n) = A000217(n+3)-1, a(4+4*n) = A000217(n+4)-1. - Paul Curtz, Dec 23 2010.

a(n) = 3*a(n-4) - 3*a(n-8) + a(n-12). This is not the shortest recurrence. -Paul Curtz, Mar 27 2011

a(1+3*n) = numerator of 9*n*(n+1)/4 = 9*A064038(1+n). - Paul Curtz, Apr 06 2011

a(n) = n*(n+3)*(3-i^(n*(n-1)))/8, where i=sqrt(-1).  - Bruno Berselli, Apr 07 2011

EXAMPLE

0, 1, 5/2, 9/2, 7, 10, 27/2, 35/2, 22, 27, ...

MATHEMATICA

f[n_] := n/GCD[n, 4]; Array[f[#] f[# + 3] &, 58]

Rest[CoefficientList[Series[x^2*(-1 - 2*x - 5*x^4 + 3*x^5 - 2*x^6 + x^7)/((x - 1)^3*(x^2 + 1)^3), {x, 0, 50}], x]] (* G. C. Greubel, Sep 21 2018 *)

PROG

(PARI) s=vector(40, n, 1/4*(n+2)*(n-1)) /* fractions */

vector(#s, n, numerator(s[n])) /* this sequence */ \\ Joerg Arndt, Jan 04 2011

(PARI) x='x+O('x^50); concat([0], Vec(x^2*(-1 - 2*x - 5*x^4 + 3*x^5 - 2*x^6 + x^7)/((x - 1)^3*(x^2 + 1)^3))) \\ G. C. Greubel, Sep 21 2018

(MAGMA) m:=50; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(x^2*(-1 - 2*x - 5*x^4 + 3*x^5 - 2*x^6 + x^7)/((x - 1)^3*(x^2 + 1)^3))); // G. C. Greubel, Sep 21 2018

CROSSREFS

Cf. A130658 (denominators), A033954 (quadrisection), A001107 (quadrisection), A181890 (quadrisection).

Sequence in context: A077125 A233831 A232190 * A055566 A255247 A153610

Adjacent sequences:  A160047 A160048 A160049 * A160051 A160052 A160053

KEYWORD

nonn,easy,frac

AUTHOR

Eric W. Weisstein, Apr 30 2009

EXTENSIONS

Edited by N. J. A. Sloane, Dec 23 2010

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 4 17:59 EST 2020. Contains 338935 sequences. (Running on oeis4.)