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A121800
a(n)= 4*a(n-1) +18*a(n-2) -48*a(n-3) -60*a(n-4) +80*a(n-5) +56*a(n-6).
0
0, 159, 4694, 36506, 190224, 1152620, 6013304, 33863688, 180138368, 989566320, 5317362784, 28948792992, 156246056704, 847762543808, 4584148419456, 24840385901696, 134422525407232, 728032988040960, 3940920763725312
OFFSET
1,2
COMMENTS
As indicated by the generating function, this can be written as a linear combination of A007070, A081180 and A000079. [Oct 14 2009]
FORMULA
G.f.: x^2*(-159-4058*x-14868*x^2+32660*x^3+30532*x^4)/( (2*x^2-1) * (2*x^2+4*x+1) * ( 14*x^2-8*x+1)). [Oct 14 2009]
MATHEMATICA
M = {{0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0}, {1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0}, {1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0}, {1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0}, {0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0}, {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1}, {0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1}, {0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0}}; v[1] = Table[Fibonacci[n], {n, 0, 17}] v[n_] := v[n] = M.v[n - 1] a = Table[v[n][[1]], {n, 1, 50}]
LinearRecurrence[{4, 18, -48, -60, 80, 56}, {0, 159, 4694, 36506, 190224, 1152620}, 40] (* Harvey P. Dale, May 13 2012 *)
CROSSREFS
Sequence in context: A227709 A212780 A232408 * A121804 A293920 A281336
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Aug 27 2006
EXTENSIONS
Definition replaced by recurrence - The Assoc. Editors of the OEIS, Oct 14 2009
STATUS
approved