This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A242300 a(n) = Sum_{0<=i
 0, 2, 11, 35, 105, 292, 796, 2130, 5655, 14927, 39281, 103160, 270600, 709282, 1858291, 4867275, 12746265, 33375932, 87388676, 228801650, 599034975, 1568333527, 4106014561, 10749789360, 28143481680, 73680863042, 192899442971, 505018008755, 1322155461705 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This sequence does for Lucas numbers what A190173 does for Fibonacci numbers. LINKS Index entries for linear recurrences with constant coefficients, signature (4,-2,-6,4,2,-1). FORMULA The sums are (1) for L(2*k): (L(2*k+1)-1)^2 + L(2*k-1) + 1 and (2) for L(2*k+1): (L(2*k+2)-1)^2 + L(2*k) - 4. G.f.: -x*(x^3+5*x^2-3*x-2) / ((x-1)*(x+1)*(x^2-3*x+1)*(x^2+x-1)). - Colin Barker, May 12 2014 a(n) = (L(n+1)-1)^2 + L(n-1) + (5*(-1)^n-3)/2. - Colin Barker, May 13 2014 EXAMPLE For L(12) = a(13) the sum is (L(13)-1)^2 + L(11) + 1 = 520^2 + 200 = 270600 and for L(13) = a(14) the sum is (L(14)-1)^2 + l(12) - 4 = 842^2 + 322 - 4 = 709282. PROG (PARI) concat(0, Vec(-x*(x^3+5*x^2-3*x-2)/((x-1)*(x+1)*(x^2-3*x+1)*(x^2+x-1)) + O(x^100))) \\ Colin Barker, May 13 2014 (Sage) [(lucas_number2(i+1, 1, -1)-1)^2+lucas_number2(i-1, 1, -1)+(5*(-1)^i-3)/2 for i in [0..50]] # Tom Edgar, May 13 2014 CROSSREFS Cf. A000032, A190173. Sequence in context: A000914 A256317 A086735 * A078982 A154416 A184538 Adjacent sequences:  A242297 A242298 A242299 * A242301 A242302 A242303 KEYWORD nonn,easy AUTHOR J. M. Bergot, May 10 2014 EXTENSIONS Typo in a(18) fixed by Colin Barker, May 12 2014 More terms from Colin Barker, May 12 2014 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 12 19:19 EST 2018. Contains 317116 sequences. (Running on oeis4.)