The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (1,2,-1,-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. A000032, A074331. Cf. A004146. Sequence in context: A248699 A032006 A167158 * A284428 A096976 A052547 Adjacent sequences:  A074389 A074390 A074391 * A074393 A074394 A074395 KEYWORD nonn,easy AUTHOR Mario Catalani (mario.catalani(AT)unito.it), Aug 22 2002 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 30 23:34 EDT 2020. Contains 334747 sequences. (Running on oeis4.)