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A014523
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Number of Hamiltonian paths in a 4 X (2n+1) grid.
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0
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1, 4, 20, 111, 624, 3505, 19676, 110444, 619935, 3479776, 19532449, 109638260, 615414276, 3454402959, 19390027600, 108838828241, 610926955724, 3429215026140, 19248644351551, 108045225087424, 606472354675265
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| K. L. Collins and L. B. Krompart, The number of Hamiltonian paths in a rectangular grid, Discrete Math. 169 (1997), 29-38.
Michael Dougherty, Christopher French, Benjamin Saderholm, and Wenyang Qian, Hankel Transforms of Linear Combinations of Catalan Numbers, Journal of Integer Sequences, Vol. 14 (2011), Article 11.5.1
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LINKS
| Index entries for two-way infinite sequences
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FORMULA
| G.f.: (1-3x+x^2)/(1-7x+9x^2-7x^3+x^4). a(n)=7a(n-1)-9a(n-2)+7a(n-3)-a(n-4)=-a(-2-n).
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PROG
| (PARI) {a(n)= if(n<-1, -a(-2-n), polcoeff( (1-3*x+x^2)/ (1-7*x+9*x^2-7*x^3+x^4) +x*O(x^n), n))} /* Michael Somos Jun 14 2003 */
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CROSSREFS
| Sequence in context: A158827 A026156 A025183 * A153299 A081335 A136783
Adjacent sequences: A014520 A014521 A014522 * A014524 A014525 A014526
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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