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 A190173 a(n) = Sum_{1 <= i < j <= n} F(i)*F(j), where F(k) is the k-th Fibonacci number. 10
 0, 1, 5, 17, 52, 148, 408, 1101, 2937, 7777, 20504, 53912, 141520, 371113, 972573, 2547825, 6672876, 17473996, 45754280, 119797205, 313650865, 821177281, 2149916400, 5628629232, 14736064032, 38579712913, 101003317493, 264430632401, 692289215332, 1812438042052 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Vincenzo Librandi and Bruno Berselli, Table of n, a(n) for n = 1..1000 (First 211 terms from Vincenzo Librandi) Index entries for linear recurrences with constant coefficients, signature (4,-2,-6,4,2,-1). FORMULA a(n) = F(n+1)^2 - F(n+2) + (1-(-1)^n)/2. G.f.: x^2*(1+x-x^2)/((1-x)*(1+x)*(1-x-x^2)*(1-3*x+x^2)). - Bruno Berselli, Jun 20 2012 EXAMPLE a(4) = F(1)*F(2) + F(1)*F(3) + F(1)*F(4) + F(2)*F(3) + F(2)*F(4) + F(3)*F(4) = 1 + 2 + 3 + 2 + 3 + 6 = 17. MAPLE with(combinat): seq(fibonacci(n+1)^2-fibonacci(n+2)+1/2-(1/2)*(-1)^n, n = 1 .. 30); MATHEMATICA Table[Fibonacci[n + 1]^2 - Fibonacci[n + 1] + (1 - (-1)^n)/2, {n, 1, 50}] (* G. C. Greubel, Mar 04 2017 *) PROG (MAGMA) [Fibonacci(n+1)^2 - Fibonacci(n+2) + (1-(-1)^n)/2: n in [1..30]]; // Vincenzo Librandi, Jun 05 2011 (PARI) a(n)=fibonacci(n+1)^2-fibonacci(n+2)+n%2 \\ Charles R Greathouse IV, Jun 08 2011 CROSSREFS Cf. A000045. Sequence in context: A137500 A146814 A034335 * A187257 A290186 A178703 Adjacent sequences:  A190170 A190171 A190172 * A190174 A190175 A190176 KEYWORD nonn,easy AUTHOR Emeric Deutsch, May 31 2011 STATUS approved

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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)