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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.
2
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
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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Formula adapted to the offset from Bruno Berselli, Aug 27 2013
STATUS
approved