login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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
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
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 * A370679 A042627 A042624
KEYWORD
nonn,easy
AUTHOR
STATUS
approved