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A006864 Number of Hamiltonian cycles in P_4 X P_n.
(Formerly M1603)
6
0, 1, 2, 6, 14, 37, 92, 236, 596, 1517, 3846, 9770, 24794, 62953, 159800, 405688, 1029864, 2614457, 6637066, 16849006, 42773094, 108584525, 275654292, 699780452, 1776473532, 4509783909, 11448608270, 29063617746, 73781357746, 187302518353, 475489124976 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Wazir tours on a 4 X n grid. There are two closed loops for a 4x4 board, appearing as an H and a C, for example. - Ed Pegg Jr, Sep 07 2010
REFERENCES
F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.
Kwong, Y. H. H.; Enumeration of Hamiltonian cycles in P_4 X P_n and P_5 X P_n. Ars Combin. 33 (1992), 87-96.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Tosic R., Bodroza O., Harris Kwong Y. H. and Joseph Straight H., On the number of Hamiltonian cycles of P4 X Pn, Indian J. Pure Appl. Math. 21 (5) (1990), 403-409.
LINKS
F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.
C. Flye Sainte-Marie, Manières différentes de tracer une route fermée ..., L'Intermédiaire des Mathématiciens, vol. 11 (1904), pp. 86-88 (in French).
George Jelliss, Wazir Wanderings
FORMULA
a(n) = 2*a(n-1) + 2*a(n-2) - 2*a(n-3) + a(n-4).
G.f.: x^2/(1-2x-2x^2+2x^3-x^4). - R. J. Mathar, Dec 16 2008
a(n)=sum ( sum ( binomial(k,j) * sum (binomial(j, i-j)*2^j *binomial(k-j,n-i-3*(k-j))*(-2)^(4*(k-j)-(n-i)), i,j,n-k+j) , j,0,k) , k,1,n ), n>0. - Vladimir Kruchinin, Aug 04 2010
a(n) = Sum_{k=1..n-1} A181688(k). - Kevin McShane, Aug 04 2019
PROG
(Maxima) a(n):=sum ( sum ( binomial(k, j) *sum (binomial(j, i-j)*2^j *binomial(k-j, n-i-3*(k-j))*(-2)^(4*(k-j)-(n-i)), i, j, n-k+j) , j, 0, k) , k, 1, n ); /* Vladimir Kruchinin, Aug 04 2010 */
CROSSREFS
Sequence in context: A248113 A339985 A026598 * A217420 A071636 A263758
KEYWORD
easy,nonn
AUTHOR
kwong(AT)cs.fredonia.edu (Harris Kwong), N. J. A. Sloane, Simon Plouffe and Frans J. Faase
STATUS
approved

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Last modified March 19 07:21 EDT 2024. Contains 370955 sequences. (Running on oeis4.)