This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A188378 Partial sums of A005248. 4
 2, 5, 12, 30, 77, 200, 522, 1365, 3572, 9350, 24477, 64080, 167762, 439205, 1149852, 3010350, 7881197, 20633240, 54018522, 141422325, 370248452, 969323030, 2537720637, 6643838880, 17393796002, 45537549125, 119218851372, 312119004990, 817138163597, 2139295485800 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Different from A024851. LINKS Robert Israel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (4,-4,1) FORMULA a(n) = A002878(n)+1 = 2*A027941(n+1)-3*A027941(n). G.f. ( -2+3*x ) / ( (x-1)*(x^2-3*x+1) ). - R. J. Mathar, Mar 30 2011 a(n) = 5*A001654(n) + 1 + (-1)^n, n>=0. [Wolfdieter Lang, Jul 23 2012] (a(n)^3 + (a(n)-2)^3) / 2 = A000032(A016945(n)) = Lucas(6n+3) = A267797(n), for n>0. - Altug Alkan, Jan 31 2016 a(n) = 2^(-1-n)*(2^(1+n)-(3-sqrt(5))^n*(-1+sqrt(5))+(1+sqrt(5))*(3+sqrt(5))^n). - Colin Barker, Nov 02 2016 MAPLE f:= gfun:-rectoproc({a(n+3)-4*a(n+2)+4*a(n+1)-a(n), a(0) = 2, a(1) = 5, a(2) = 12}, a(n), remember): map(f, [\$0..60]); # Robert Israel, Feb 02 2016 MATHEMATICA LinearRecurrence[{4, -4, 1}, {2, 5, 12}, 30] (* Harvey P. Dale, Oct 05 2015 *) Accumulate@ LucasL@ Range[0, 58, 2] (* Michael De Vlieger, Jan 24 2016 *) PROG (PARI) a(n) = 5*fibonacci(n)*fibonacci(n+1) + 1 + (-1)^n; \\ Michel Marcus, Aug 26 2013 (PARI) Vec((-2+3*x)/((x-1)*(x^2-3*x+1)) + O(x^100)) \\ Altug Alkan, Jan 24 2016 (MAGMA) [5*Fibonacci(n)*Fibonacci(n+1)+1+(-1)^n: n in [0..40]]; // Vincenzo Librandi, Jan 24 2016 CROSSREFS Cf. A267797. - Altug Alkan, Jan 31 2016 Sequence in context: A086622 A253831 A024851 * A145267 A103287 A136704 Adjacent sequences:  A188375 A188376 A188377 * A188379 A188380 A188381 KEYWORD nonn,easy AUTHOR Gabriele Fici, Mar 29 2011 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 July 19 08:23 EDT 2019. Contains 325155 sequences. (Running on oeis4.)