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a(n) = (n + 4)*4^(n-1). - Paolo P. Lava, Jul 08 2008
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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
More terms from Stefano Spezia, Mar 05 2023
<a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-16).
a(n) = (1/4)*(n-1)* + 4^(n-1)+*4^(n-1), with n>=1. - Paolo P. Lava, Jul 08 2008
a(0) = 1, a(n) = (n + 4)*4^(n-1) for n >= 1.
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]
G.f.: (1 - 3*x)/(1 - 4*x)^2 . - Philippe Deléham, Dec 11 2008
E.g.f.: exp(4*x)*(1 + x). - Stefano Spezia, Mar 05 2023
nonn,easy
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