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A028478 Number of perfect matchings in graph C_{7} X P_{2n}. 3
1, 29, 1471, 79808, 4375897, 240378643, 13209069847, 725898384359, 39891876471539, 2192269974717929, 120476898663671488, 6620847045486150863, 363850801995789860221, 19995539171949615541457, 1098861359580093467365169, 60388283471627147242052029 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500

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

FORMULA

G.f.: (x^7 -42*x^6 +364*x^5 -1001*x^4 +1001*x^3 -364*x^2 +42*x -1)/( -x^8 +71*x^7 -952*x^6 +3976*x^5 -6384*x^4 +3976*x^3 -952*x^2 +71*x -1). - Alois P. Heinz, Dec 09 2013

a(n) = 2^n * sqrt(Resultant(U_{2*n}(x/2), T_{7}(i*x/2))), where T_n(x) is a Chebyshev polynomial of the first kind, U_n(x) is a Chebyshev polynomial of the second kind and i = sqrt(-1). - Seiichi Manyama, Apr 17 2020

PROG

(PARI) {a(n) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(7, 1, I*x/2)))} \\ Seiichi Manyama, Apr 17 2020

CROSSREFS

Sequence in context: A049657 A091994 A126555 * A042627 A042624 A190826

Adjacent sequences:  A028475 A028476 A028477 * A028479 A028480 A028481

KEYWORD

nonn,easy

AUTHOR

Per H. Lundow

STATUS

approved

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Last modified July 29 22:13 EDT 2021. Contains 346346 sequences. (Running on oeis4.)