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

0,6

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).

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

Adjacent sequences: A228580 A228581 A228582 * A228584 A228585 A228586

Keyword

nonn,easy

Author

Yosu Yurramendi, María Merino, Aug 26 2013

Extensions

More terms from Vincenzo Librandi, Sep 04 2013

Status

approved