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A074392
a(n) = Lucas(n+1) + (3*(-1)^n - 1)/2.
3
2, 1, 5, 5, 12, 16, 30, 45, 77, 121, 200, 320, 522, 841, 1365, 2205, 3572, 5776, 9350, 15125, 24477, 39601, 64080, 103680, 167762, 271441, 439205, 710645, 1149852, 1860496, 3010350, 4870845, 7881197, 12752041, 20633240, 33385280, 54018522
OFFSET
0,1
FORMULA
a(n) = Sum (L(2i+e), (i=0, 1, .., Floor(n/2))), where L(n) are Lucas numbers and e=2(n/2 - Floor(n/2)).
Convolution of L(n) with the sequence (1, 0, 1, 0, 1, 0, ...)
a(n) = a(n-1) + 2*a(n-2) - a(n-3) - a(n-4) for n>3.
G.f.: ( 2-x ) / ( (x-1)*(1+x)*(x^2+x-1) ).
a(n) = 2*A052952(n)-A052952(n-1). - R. J. Mathar, Oct 04 2013
a(n) = 2^(-1-n) * (3*(-2)^n - 2^n + (1-sqrt(5))^(1+n) + (1+sqrt(5))^(1+n)). - Colin Barker, Jul 12 2017
MATHEMATICA
CoefficientList[Series[(2-x)/(1-x-2*x^2+x^3+x^4), {x, 0, 40}], x]
PROG
(PARI) Vec((2-x) / ((x-1)*(1+x)*(x^2+x-1)) + O(x^50)) \\ Colin Barker, Jul 12 2017
CROSSREFS
Cf. A004146.
Sequence in context: A032006 A377806 A167158 * A284428 A096976 A052547
KEYWORD
nonn,easy
AUTHOR
Mario Catalani (mario.catalani(AT)unito.it), Aug 22 2002
STATUS
approved