A028472 Number of perfect matchings in graph P_{10} X P_{n}.

1, 1, 89, 571, 18061, 185921, 4213133, 53175517, 1031151241, 14479521761, 258584046368, 3852472573499, 65743732590821, 1012747193318519, 16848161392724969, 264499788583572499, 4337452956682508609, 68829675768134027209, 1119577238373960926141

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.

Index entries for linear recurrences with constant coefficients, signature (1, 285, 411, -18027, -20689, 472275, 271027, -6149853, -471319, 42303393, -10402780, -157353820, 58545372, 335484428, -123321948, -429447820, 123321948, 335484428, -58545372, -157353820, 10402780, 42303393, 471319, -6149853, -271027, 472275, 20689, -18027, -411, 285, -1, -1).

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

Mathematica

T[_?OddQ, _?OddQ] = 0;
T[m_, n_] := Product[2(2+Cos[2 j Pi/(m+1)]+Cos[2 k Pi/(n+1)]), {k, 1, n/2}, {j, 1, m/2}];
a[n_] := T[n, 10] // Round;
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, May 28 2022 *)

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