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A289877
Number of maximal cliques in the n-triangular honeycomb queen graph.
0
1, 8, 19, 36, 60, 93, 136, 191, 259, 342, 441, 558, 694, 851, 1030, 1233, 1461, 1716, 1999, 2312, 2656, 3033, 3444, 3891, 4375, 4898, 5461, 6066, 6714, 7407, 8146, 8933, 9769, 10656, 11595, 12588, 13636, 14741, 15904, 17127
OFFSET
2,2
COMMENTS
Using the formula to extend to a(1) gives -3, while the 1-triangular honeycomb grid graph has 1 maximal clique.
LINKS
FORMULA
a(n) = (2*n*(22 - n + 2*n^2) - 95 - (-1)^n)/16.
a(n) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5).
G.f.: (x^2*(1 + 5*x - 3*x^2 - 3*x^3 + 3*x^4))/((-1 + x)^4*(1 + x)).
MATHEMATICA
Table[(2 n (22 - n + 2 n^2) - 95 - (-1)^n)/16, {n, 2, 20}]
LinearRecurrence[{3, -2, -2, 3, -1}, {1, 8, 19, 36, 60, 93}, 20]
CoefficientList[Series[(1 + 5 x - 3 x^2 - 3 x^3 + 3 x^4)/((-1 + x)^4 (1 + x)), {x, 0, 20}], x]
PROG
(PARI) a(n)=(2*n*(2*n^2-n+22)-95+1)>>4 \\ Charles R Greathouse IV, Jul 14 2017
CROSSREFS
Sequence in context: A135027 A158916 A045557 * A089111 A127873 A192975
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jul 14 2017
STATUS
approved