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A228581 The number of binary pattern classes in the (2,n)-rectangular grid with 6 '1's and (2n-6) '0's: two patterns are in same class if one of them can be obtained by a reflection or 180-degree rotation of the other.

%I A228581 #18 Sep 08 2022 08:46:05
%S A228581 0,0,0,1,10,60,246,777,2044,4704,9780,18777,33814,57772,94458,148785,
%T A228581 226968,336736,487560,690897,960450,1312444,1765918,2343033,3069396,
%U A228581 3974400,5091580,6458985,8119566,10121580,12519010,15372001,18747312,22718784,27367824,32783905
%N A228581 The number of binary pattern classes in the (2,n)-rectangular grid with 6 '1's and (2n-6) '0's: two patterns are in same class if one of them can be obtained by a reflection or 180-degree rotation of the other.
%C A228581 Column 6 of A226048.
%H A228581 Vincenzo Librandi, <a href="/A228581/b228581.txt">Table of n, a(n) for n = 0..1000</a>
%F A228581 a(n) = (1/4)*( binomial(2*n,6) + 3*binomial(n,3) ).
%F A228581 a(n) = 7*a(n-1) -21*a(n-2) +35*a(n-3) -35*a(n-4) +21*a(n-5) -7*a(n-6) +a(n-7) with n>6, a(0)=a(1)=a(2)=0, a(3)=1, a(4)=10, a(5)=60, a(6)=246.
%F A228581 G.f.: x^3*(1+3*x+11*x^2+x^3)/(1-x)^7. [_Bruno Berselli_, Aug 27 2013]
%t A228581 CoefficientList[Series[x^3 (1 + 3 x + 11 x^2 + x^3) / (1 - x)^7, {x, 0, 50}], x] (* _Vincenzo Librandi_, Sep 04 2013 *)
%o A228581 (R) a <- 0
%o A228581     for(n in 1:40) a[n+1] <- (1/4)*(choose(2*n, 6) + 3*choose(n,3))     a
%o A228581 (Magma) [(1/4)*(Binomial(2*n,6) + 3*Binomial(n,3)): n in [0..50]]; // _Vincenzo Librandi_, Sep 04 2013
%Y A228581 Cf. A226048.
%K A228581 nonn,easy
%O A228581 0,5
%A A228581 _Yosu Yurramendi_, _María Merino_, Aug 26 2013
%E A228581 More terms from _Vincenzo Librandi_, Sep 04 2013