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A028472 Number of perfect matchings in graph P_{10} X P_{n}. 3
1, 1, 89, 571, 18061, 185921, 4213133, 53175517, 1031151241, 14479521761, 258584046368, 3852472573499, 65743732590821, 1012747193318519, 16848161392724969, 264499788583572499, 4337452956682508609, 68829675768134027209, 1119577238373960926141 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..18.

J. L. Hock and R. B. McQuistan, A note on the occupational degeneracy for dimers on a saturated two-dimensional lattice space, Discrete Applied Mathematics, 1984, v.8, 101-104.

Per Hakan Lundow, Computation of matching polynomials and the number of 1-factors in polygraphs, Research report, No 12, 1996, Department of Math., Umea University, Sweden.

Per Hakan Lundow, Enumeration of matchings in polygraphs, 1998.

FORMULA

G.f.: (1 - 197x^2 - 214x^3 + 9741x^4 + 7262x^5 - 202037x^6 - 56736x^7 + 2064705x^8 - 156848x^9 - 11058754x^10 + 2972710x^11 + 32425754x^12 - 10324398x^13 - 54699758x^14 + 15137114x^15 + 54699758x^16 - 10324398x^17 - 32425754x^18 + 2972710x^19 + 11058754x^20 - 156848x^21 - 2064705x^22 - 56736x^23 + 202037x^24 + 7262x^25 - 9741x^26 - 214x^27 + 197x^28 - x^30)/(1 - x - 285x^2 - 411x^3 + 18027x^4 + 20689x^5 - 472275x^6 - 271027x^7 + 6149853x^8 + 471319x^9 - 42303393x^10 + 10402780x^11 + 157353820x^12 - 58545372x^13 - 335484428x^14 + 123321948x^15 + 429447820x^16 - 123321948x^17 - 335484428x^18 + 58545372x^19 + 157353820x^20 - 10402780x^21 - 42303393x^22 - 471319x^23 + 6149853x^24 + 271027x^25 - 472275x^26 - 20689x^27 + 18027x^28 + 411x^29 - 285x^30 + x^31 + x^32). - Sergey Perepechko, Nov 27 2012

PROG

(PARI) {a(n) = sqrtint(polresultant(polchebyshev(10, 2, x/2), polchebyshev(n, 2, I*x/2)))} \\ Seiichi Manyama, Apr 13 2020

CROSSREFS

Row 10 of array A099390.

Sequence in context: A141866 A176634 A224740 * A136646 A142566 A063654

Adjacent sequences:  A028469 A028470 A028471 * A028473 A028474 A028475

KEYWORD

nonn

AUTHOR

Per H. Lundow

STATUS

approved

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Last modified June 5 12:47 EDT 2020. Contains 334840 sequences. (Running on oeis4.)