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Search: id:A082762
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| 1, 8, 44, 232, 1216, 6368, 33344, 174592, 914176, 4786688, 25063424, 131233792, 687149056, 3597959168, 18839158784, 98643116032, 516502061056, 2704439902208, 14160631169024, 74146027405312, 388233639755776
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OFFSET
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0,2
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FORMULA
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a(n) = Sum[ Trinomial[n, k] Lucas[k+1], {k, 0, 2n} ] where Trinomial[n, k] = trinomial coefficients (A027907)
a(n) = 2^n Lucas[2n+1] where Lucas[n] = Lucas numbers (A000032).
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
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]
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CROSSREFS
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Sequence in context: A003220 A125318 A000373 this_sequence A147828 A155604 A126476
Adjacent sequences: A082759 A082760 A082761 this_sequence A082763 A082764 A082765
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KEYWORD
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easy,nonn
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AUTHOR
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Emanuele Munarini (munarini(AT)mate.polimi.it), May 21 2003
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