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 A327728 Number of unlabeled multigraphs with loops allowed and n edges covering three vertices. 2
 0, 2, 8, 19, 40, 77, 132, 217, 340, 510, 742, 1054, 1456, 1976, 2634, 3453, 4464, 5703, 7194, 8987, 11120, 13636, 16588, 20036, 24024, 28630, 33916, 39951, 46816, 54601, 63376, 73253, 84324, 96690, 110466, 125778, 142728, 161468, 182126, 204841, 229768, 257075, 286902, 319447, 354880, 393384 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (2,1,-2,-3,0,6,0,-3,-2,1,2,-1). FORMULA a(n) = A050531(n) - A002620(n+2). a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - 3*a(n-4) + 6*a(n-6) - 3*a(n-8) - 2*a(n-9) + a(n-10) + 2*a(n-11) - a(n-12) for n > 12. G.f.: x^2*(2 + 4*x + x^2 - 2*x^3 + x^6)/((1 - x)^6*(1 + x)^2*(1 + x + x^2)^2). EXAMPLE a(2) = 2 since three vertices may be covered with two edges in 2 ways: the path graph P(3) or an edge plus a loop. PROG (PARI) concat([0], Vec((2 + 4*x + x^2 - 2*x^3 + x^6)/((1 - x)^6*(1 + x)^2*(1 + x + x^2)^2) + O(x^40))) CROSSREFS Column k=3 of A327615. Cf. A002620, A050531. Sequence in context: A193389 A030504 A240279 * A000158 A101427 A286269 Adjacent sequences: A327725 A327726 A327727 * A327729 A327730 A327731 KEYWORD nonn,easy AUTHOR Andrew Howroyd, Oct 23 2019 STATUS approved

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Last modified March 4 05:23 EST 2024. Contains 370522 sequences. (Running on oeis4.)