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%I #34 Aug 28 2024 04:18:25
%S 0,33,702,3630,11409,27603,56748,104352,176895,281829,427578,623538,
%T 880077,1208535,1621224,2131428,2753403,3502377,4394550,5447094,
%U 6678153,8106843,9753252,11638440,13784439,16214253,18951858,22022202,25451205,29265759,33493728
%N Number of ways two dihexes can be placed on an n-th regular hexagonal board.
%H Paolo Xausa, <a href="/A372855/b372855.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = (3/2)*(27*n^4 - 90*n^3 + 78*n^2 + 11*n - 24), for n > 1.
%F a(n) = 5*a(n - 1) - 10*a(n - 2) + 10*a(n - 3) - 5*a(n - 4) + a(n - 5) for n > 6.
%F G.f.: 3*x^2*(11 + 179*x + 150*x^2 - 17*x^3 + x^4)/(1 - x)^5.
%F E.g.f.: 36 - 3*x + 3*exp(x)*(27*x^4 + 72*x^3 - 3*x^2 + 26*x - 24)/2. - _Stefano Spezia_, Jun 04 2024
%e Regular hexagonal boards n = 1...4:
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%e For n = 2 the a(2) = 33: (without grid)
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%t LinearRecurrence[{5, -10, 10, -5, 1}, {0, 33, 702, 3630, 11409, 27603}, 50] (* _Paolo Xausa_, Aug 28 2024 *)
%Y Cf. A000384, A242856.
%K nonn,easy
%O 1,2
%A _Nicolas Bělohoubek_, May 15 2024