|
| |
|
|
A109500
|
|
Number of closed walks of length n on the complete graph on 6 nodes from a given node.
|
|
12
|
|
|
|
1, 0, 5, 20, 105, 520, 2605, 13020, 65105, 325520, 1627605, 8138020, 40690105, 203450520, 1017252605, 5086263020, 25431315105, 127156575520, 635782877605, 3178914388020, 15894571940105, 79472859700520
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
LINKS
|
G. C. Greubel, Table of n, a(n) for n = 0..1000
Ji Young Choi, A Generalization of Collatz Functions and Jacobsthal Numbers, J. Int. Seq., Vol. 21 (2018), Article 18.5.4.
Index entries for linear recurrences with constant coefficients, signature (4,5).
|
|
|
FORMULA
|
G.f.: (1 - 4*x)/(1 - 4*x - 5*x^2).
a(n) = (5^n + 5*(-1)^n)/6.
a(n) = 5^(n-1) - a(n-1), a(0) = 1. - Jon E. Schoenfield, Feb 08 2015
|
|
|
MATHEMATICA
|
k=0; lst={k}; Do[k=5^n-k; AppendTo[lst, k], {n, 1, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 11 2008 *)
CoefficientList[Series[(1 - 4*x)/(1 - 4*x - 5*x^2), {x, 0, 50}], x] (* or *) Table[(5^n + 5*(-1)^n)/6, {n, 0, 30}] (* G. C. Greubel, Dec 30 2017 *)
|
|
|
PROG
|
(PARI) for(n=0, 30, print1((5^n + 5*(-1)^n)/6, ", ")) \\ G. C. Greubel, Dec 30 2017
(MAGMA) [(5^n + 5*(-1)^n)/6: n in [0..30]]; // G. C. Greubel, Dec 30 2017
|
|
|
CROSSREFS
|
Cf. A109502.
Cf. sequences with the same recurrence form: A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531. - Vladimir Joseph Stephan Orlovsky, Dec 11 2008
Sequence in context: A276314 A292358 A259275 * A137961 A334716 A167145
Adjacent sequences: A109497 A109498 A109499 * A109501 A109502 A109503
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Mitch Harris, Jun 30 2005
|
|
|
EXTENSIONS
|
Corrected by Franklin T. Adams-Watters, Sep 18 2006
Edited by Jon E. Schoenfield, Feb 08 2015
|
|
|
STATUS
|
approved
|
| |
|
|
