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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A300847 a(n) = 12*binomial(n, 5). 0
0, 0, 0, 0, 0, 12, 72, 252, 672, 1512, 3024, 5544, 9504, 15444, 24024, 36036, 52416, 74256, 102816, 139536, 186048, 244188, 316008, 403788, 510048, 637560, 789360, 968760, 1179360, 1425060, 1710072, 2038932, 2416512, 2848032, 3339072, 3895584, 4523904, 5230764 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Also the number of 5-cycles in the complete graph K_n for n >= 1.

LINKS

Table of n, a(n) for n=0..37.

Eric Weisstein's World of Mathematics, Complete Graph

Eric Weisstein's World of Mathematics, Graph Cycle

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

FORMULA

G.f.: 12*x^5/(x - 1)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) + 6*a(n-4) - a(n-5).

a(n) = A052787(n)/10 = 12*A000389(n).

a(n) = (n - 4)*(n - 3)*(n - 2)*(n - 1)*n/10.

MATHEMATICA

Table[12 Binomial[n, 5], {n, 0, 20}]

12 Binomial[Range[0, 20], 5]

LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 0, 0, 0, 12, 72}, {0, 20}]

CoefficientList[Series[12 x^5/(x - 1)^6, {x, 0, 20}], x]

PROG

(PARI) a(n) = 12*binomial(n, 5); \\ Altug Alkan, Mar 13 2018

CROSSREFS

Cf. A000389, A052787.

Sequence in context: A199531 A188660 A047928 * A235870 A008533 A010024

Adjacent sequences:  A300844 A300845 A300846 * A300848 A300849 A300850

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Mar 13 2018

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 September 25 04:20 EDT 2021. Contains 347652 sequences. (Running on oeis4.)