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A014523 Number of Hamiltonian paths in a 4 X (2n+1) grid starting at the lower left corner and finishing in the upper right corner. 6
1, 4, 20, 111, 624, 3505, 19676, 110444, 619935, 3479776, 19532449, 109638260, 615414276, 3454402959, 19390027600, 108838828241, 610926955724, 3429215026140, 19248644351551, 108045225087424, 606472354675265, 3404210752374756, 19108292005806324 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..22.

Belgacem Bouras, A New Characterization of Catalan Numbers Related to Hankel Transforms and Fibonacci Numbers, Journal of Integer Sequences, 16 (2013), #13.3.3.

Karen L. Collins, Lucia B. Krompart, The number of Hamiltonian paths in a rectangular grid, Discrete Mathematics, Volume 169, Issues 1-3, 15 May 1997, Pages 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.

Index entries for two-way infinite sequences

Index entries for sequences related to graphs, Hamiltonian

Index entries for linear recurrences with constant coefficients, signature (7,-9,7,-1).

FORMULA

G.f.: (1-3*x+x^2)/(1-7*x+9*x^2-7*x^3+x^4).

a(n) = 7*a(n-1) - 9*a(n-2) + 7*a(n-3) - a(n-4) = -a(-2-n).

MATHEMATICA

CoefficientList[Series[(1 - 3 x + x^2)/(1 - 7 x + 9 x^2 - 7 x^3 + x^4), {x, 0, 50}], x] (* Vincenzo Librandi, Dec 21 2015 *)

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 */

(MAGMA) I:=[1, 4, 20, 111]; [n le 4 select I[n] else 7*Self(n-1)- 9*Self(n-2)+7*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 21 2015

CROSSREFS

Cf. A014584.

Sequence in context: A263854 A026156 A025183 * A153299 A239643 A081335

Adjacent sequences:  A014520 A014521 A014522 * A014524 A014525 A014526

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Dec 11 1999

EXTENSIONS

Sequence name clarified by Andrew Howroyd, Dec 20 2015

a(21)-a(22) from Vincenzo Librandi, Dec 21 2015

STATUS

approved

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Last modified July 5 05:47 EDT 2022. Contains 355087 sequences. (Running on oeis4.)