login
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.
2
0, 0, 0, 1, 10, 60, 246, 777, 2044, 4704, 9780, 18777, 33814, 57772, 94458, 148785, 226968, 336736, 487560, 690897, 960450, 1312444, 1765918, 2343033, 3069396, 3974400, 5091580, 6458985, 8119566, 10121580, 12519010, 15372001, 18747312, 22718784, 27367824, 32783905
OFFSET
0,5
COMMENTS
Column 6 of A226048.
LINKS
FORMULA
a(n) = (1/4)*( binomial(2*n,6) + 3*binomial(n,3) ).
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.
G.f.: x^3*(1+3*x+11*x^2+x^3)/(1-x)^7. [Bruno Berselli, Aug 27 2013]
MATHEMATICA
CoefficientList[Series[x^3 (1 + 3 x + 11 x^2 + x^3) / (1 - x)^7, {x, 0, 50}], x] (* Vincenzo Librandi, Sep 04 2013 *)
PROG
(R) a <- 0
for(n in 1:40) a[n+1] <- (1/4)*(choose(2*n, 6) + 3*choose(n, 3)) a
(Magma) [(1/4)*(Binomial(2*n, 6) + 3*Binomial(n, 3)): n in [0..50]]; // Vincenzo Librandi, Sep 04 2013
CROSSREFS
Cf. A226048.
Sequence in context: A266732 A283727 A349415 * A241929 A278721 A341366
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Sep 04 2013
STATUS
approved