|
| |
|
|
A091002
|
|
Number of walks of length n between non-adjacent nodes on the Petersen graph.
|
|
4
| |
|
|
0, 0, 1, 2, 9, 22, 77, 210, 673, 1934, 5973, 17578, 53417, 158886, 479389, 1432706, 4309041, 12905278, 38759525, 116191194, 348748345, 1045895510, 3138385581, 9413758642, 28244072129, 84726623982, 254191056757, 762550800650, 2287697141193, 6863001945094
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,4
|
|
|
COMMENTS
| 3^n=A091000(n)+3*A091001(n)+6*a(n). Binomial transform of A091005.
|
|
|
FORMULA
| G.f.: x^2/((1-x)(1+2x)(1-3x)); a(n)=3^n/10+(-2)^n/15-1/6.
a(n)=(A000244(n)-A001045(n+1)(-1)^n-4*A001045(n)(-1)^(n+1))/10.
a(n)=sum(binomial(n-k, k)*6^(k-1), k=1..n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 30 2006
|
|
|
MAPLE
| a:=n->sum(binomial(n-k, k)*6^(k-1), k=1..n): seq(a(n), n=0..27); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 30 2006
|
|
|
MATHEMATICA
| Table[(-(-2)^n + 3^n - 5)/30, {n, 40}] (* From Vladimir Joseph Stephan Orlovsky, Jun 20 2011 *)
|
|
|
PROG
| a(-2)=0, a(-1)=0, sage: from sage.combinat.sloane_functions import recur_gen2b sage: it = recur_gen2b(1, 2, 1, 6, lambda n: 1) sage: [it.next() for i in xrange(0, 29)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 03 2008
|
|
|
CROSSREFS
| Sequence in context: A023625 A166754 A026589 * A025176 A032315 A032224
Adjacent sequences: A090999 A091000 A091001 * A091003 A091004 A091005
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Dec 12 2003
|
| |
|
|
