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

0,5

Comments

Column 7 of A226048.

Links

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

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]

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 *)

Prog

(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

Crossrefs

Cf. A226048.

Sequence in context: A012642 A244730 A169833 * A128789 A356345 A053316

Adjacent sequences: A228579 A228580 A228581 * A228583 A228584 A228585

Keyword

nonn,easy

Author

Yosu Yurramendi, María Merino, Aug 26 2013

Extensions

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

Status

approved