A228582 The number of binary pattern classes in the (2,n)-rectangular grid with 7 '1's and (2n-7) '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, 2, 32, 198, 868, 2860, 7984, 19380, 42696, 86526, 164560, 296010, 509132, 841464, 1345184, 2086920, 3155472, 4660890, 6745152, 9580142, 13381940, 18407268, 24972112, 33446140, 44276440, 57979350, 75170160, 96551730

Offset: 0

Author

Yosu Yurramendi, María Merino, Aug 26 2013

Keywords

• nonn
• easy

Comments

Column 7 of A226048.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A226048.

Programs

Mathematica

CoefficientList[Series[2 x^4 (2 x^7 + 7 x^6 + 48 x^5 + 67 x^4 + 82 x^3 + 37 x^2 + 12 x + 1) / ((x + 1)^4 (x - 1)^8), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 27 2013 *)

R

a <- 0
    for(n in 1:40) a[n+1] <- (1/4)*(choose(2*(n+2), 7) + 2*choose(n+1, 3)*(1/2)*(1-(-1)^n))
    a

Formula

a(n) = (1/4)*(binomial(2*n, 7) + 2*binomial(n-1, 3)*(1/2)*(1-(-1)^n)) = (n-3)*(n-2)*(n-1)(2*n*(2n-5)*(2*n-3)*(2*n-1)-105*(-1)^n+105)/2520.

G.f.: 2*x^4*(2*x^7 +7*x^6 +48*x^5 +67*x^4 +82*x^3 +37*x^2 +12*x +1) / ((x+1)^4*(x-1)^8). [Bruno Berselli, Aug 27 2013]

Extensions

Formula adapted to the offset from Bruno Berselli, Aug 27 2013