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A079028
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a(0) = 1, a(n) = (n + 4)*4^(n-1) for n >= 1.
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6
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1, 5, 24, 112, 512, 2304, 10240, 45056, 196608, 851968, 3670016, 15728640, 67108864, 285212672, 1207959552, 5100273664, 21474836480, 90194313216, 377957122048, 1580547964928, 6597069766656, 27487790694400, 114349209288704, 474989023199232, 1970324836974592, 8162774324609024
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OFFSET
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0,2
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COMMENTS
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a(n) = det(M(n)) where M(n) is the n X n matrix defined by m(i,i) = 5, m(i,j) = i/j.
Main diagonal of array defined by m(1,j) = j; m(i,1) = i and m(i,j) = m(i-1,j) + 3*m(i-1,j-1).
4th binomial transform of (1,1,0,0,0,0,...). - Paul Barry, Mar 07 2003
Number of independent vertex subsets of the graph obtained by attaching two pendant edges to each vertex of the complete graph K_n (see A235113). Example: a(1)=5; indeed, K_1 is the one vertex graph and after attaching two pendant vertices we obtain the path graph ABC; the independent vertex subsets are: empty, {A}, {B}, {C}, and {A,C}. - Emeric Deutsch, Jan 13 2014
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LINKS
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FORMULA
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a(n) = 8*a(n-1)-16*a(n-2), a(0) = 1, a(1) = 5. - Paul Barry, Mar 07 2003
Sum_{n>=0} 1/a(n) = 1024*log(4/3) - 880/3.
Sum_{n>=0} (-1)^n/a(n) = 688/3 - 1024*log(5/4). (End)
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MATHEMATICA
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PROG
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(Sage) [lucas_number2(n, 4, 0)*n/2^10 for n in range(4, 26)] # Zerinvary Lajos, Mar 13 2009
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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