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A328652
Number of unlabeled loopless multigraphs with n edges covering four vertices.
2
0, 1, 3, 7, 13, 25, 40, 65, 99, 146, 208, 294, 399, 538, 711, 926, 1188, 1513, 1896, 2361, 2910, 3557, 4312, 5199, 6214, 7392, 8739, 10276, 12019, 14002, 16224, 18732, 21537, 24669, 28152, 32031, 36309, 41047, 46263, 51997, 58282, 65176, 72688, 80894, 89820, 99518
OFFSET
1,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (2,0,0,-2,-2,3,0,3,-2,-2,0,0,2,-1).
FORMULA
a(n) = A003082(n) - A001399(n).
a(n) = 2*a(n-1) - 2*a(n-4) - 2*a(n-5) + 3*a(n-6) + 3*a(n-8) - 2*a(n-9) - 2*a(n-10) + 2*a(n-13) - a(n-14) for n > 14.
G.f.: x^2*(1 + x + x^2 - x^3 + x^4 - 2*x^5 + 2*x^6)/((1 - x)^6*(1 + x)^2*(1 + x^2)*(1 + x + x^2)^2).
MATHEMATICA
LinearRecurrence[{2, 0, 0, -2, -2, 3, 0, 3, -2, -2, 0, 0, 2, -1}, {0, 1, 3, 7, 13, 25, 40, 65, 99, 146, 208, 294, 399, 538}, 50] (* Harvey P. Dale, Mar 06 2021 *)
PROG
(PARI) concat([0], Vec((1 + x + x^2 - x^3 + x^4 - 2*x^5 + 2*x^6)/((1 - x)^6*(1 + x)^2*(1 + x^2)*(1 + x + x^2)^2) + O(x^40)))
CROSSREFS
Column k=4 of A309936.
Sequence in context: A056764 A360783 A026103 * A301854 A092463 A259343
KEYWORD
nonn,easy
AUTHOR
Andrew Howroyd, Oct 23 2019
STATUS
approved