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A121804
1045*6^n/27-513*2^(n-2)-2072*3^(n-3)+670*(-1)^n*3^(n-3)+254*(-1)^(n+1), n>1.
0
0, 159, 4846, 43648, 272432, 1759444, 10596296, 64633588, 387979832, 2337067204, 14023337096, 84221417428, 505334268632, 3032732926564, 18196438915496, 109185158327668, 655111280131832, 3930726320267524, 23584360724983496
OFFSET
1,2
COMMENTS
Unique structure in that all the secular roots are Integers.
FORMULA
a(n)= 7*a(n-1) +5*a(n-2) -75*a(n-3) +36*a(n-4) +108*a(n-5), n>6. [Oct 14 2009]
G.f.: x^2*(-159-3733*x-8931*x^2+45409*x^3+8094*x^4)/( (6*x-1)*(3*x-1) * (2*x-1) * (3*x+1) * (1+x)). [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, 1, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0}, {0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1}, {0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1}, {0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 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[{7, 5, -75, 36, 108}, {0, 159, 4846, 43648, 272432, 1759444}, 20] (* Harvey P. Dale, May 20 2015 *)
CROSSREFS
Sequence in context: A212780 A232408 A121800 * A293920 A281336 A205164
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Aug 28 2006
EXTENSIONS
Definition replaced by formula - The Assoc. Editors of the OEIS, Oct 14 2009
STATUS
approved