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A228583
The number of binary pattern classes in the (2,n)-rectangular grid with 8 '1's and (2n-8) '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, 0, 1, 15, 135, 777, 3270, 11034, 31650, 80190, 184239, 391105, 777777, 1464255, 2630940, 4540836, 7567380, 12228780, 19229805, 29512035, 44313643, 65239845, 94345218, 134229150, 188145750, 260129610, 355138875, 479217141, 639675765, 845298235, 1106568312
OFFSET
0,6
COMMENTS
Column 8 of A226048.
LINKS
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
a(n) = (1/4)*(binomial(2*n,8) + 3*binomial(n,4)).
a(n) = 9*a(n-1)-36*a(n-2)+84*a(n-3)-126*a(n-4)+126*a(n-5)-84*a(n-6)+36*a(n-7)-9*a(n-8)+a(n-9) n>8, with a(0)=0, a(1)=0, a(2)=0, a(3)=1, a(4)=15, a(5)=135, a(6)=777, a(7)=3270, a(8)=11034.
G.f.: -x^4*(3*x^4+18*x^3+36*x^2+6*x+1) / (x-1)^9. - Colin Barker, Sep 01 2013
MATHEMATICA
CoefficientList[Series[- x^4 (3 x^4 + 18 x^3 + 36 x^2 + 6 x + 1) / (x - 1)^9, {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, 8) + 3*choose(n, 4))
a
(Magma) [(1/4)*(Binomial(2*n, 8) + 3*Binomial(n, 4)): n in [0..50]]; // Vincenzo Librandi, Sep 04 2013
CROSSREFS
Cf. A226048.
Sequence in context: A289421 A201138 A230659 * A027630 A027629 A023013
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Sep 04 2013
STATUS
approved