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.

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

Author

Yosu Yurramendi, María Merino, Aug 26 2013

Keywords

• nonn
• easy

Comments

Column 8 of A226048.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Cf. A226048.

Programs

Magma

[(1/4)*(Binomial(2*n,8) + 3*Binomial(n,4)): n in [0..50]]; // Vincenzo Librandi, Sep 04 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 *)

R

a <- 0
    for(n in 1:40) a[n+1] <- (1/4)*(choose(2*n,8) + 3*choose(n,4))
    a

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

Extensions

More terms from Vincenzo Librandi, Sep 04 2013