Search: id:A082762
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%I A082762
%S A082762 1,8,44,232,1216,6368,33344,174592,914176,4786688,25063424,131233792,
%T A082762 687149056,3597959168,18839158784,98643116032,516502061056,
%U A082762 2704439902208,14160631169024,74146027405312,388233639755776
%N A082762 Trinomial transform of Lucas numbers (A000032).
%F A082762 a(n) = Sum[ Trinomial[n, k] Lucas[k+1], {k, 0, 2n} ] where Trinomial[n, 
               k] = trinomial coefficients (A027907)
%F A082762 a(n) = 2^n Lucas[2n+1] where Lucas[n] = Lucas numbers (A000032).
%F A082762 a(n) = 2^n*A002878(n) = 2^(-n)*Sum_{k>=0} binomial(2*n+1, 2*k)*5^k; see 
               A091042 . a(0) = 1, a(1) = 8, a(n+1) = 6*a(n) - 4*a(n-1) . - DELEHAM 
               Philippe (kolotoko(AT)wanadoo.fr), Mar 01 2004
%F A082762 a(n)=(1+sqrt5)(3+sqrt5)^n+(1-sqrt5)(3-sqrt5)^n)/2 offset 0. a(n)=third 
               binomial transform of 1,5,5,25,25,125 [From Al Hakanson (hawkuu(AT)gmail.com), 
               Jul 13 2009]
%Y A082762 Sequence in context: A003220 A125318 A000373 this_sequence A147828 A155604 
               A126476
%Y A082762 Adjacent sequences: A082759 A082760 A082761 this_sequence A082763 A082764 
               A082765
%K A082762 easy,nonn
%O A082762 0,2
%A A082762 Emanuele Munarini (munarini(AT)mate.polimi.it), May 21 2003

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