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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.
11
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
OFFSET
1,3
LINKS
Vincenzo Librandi and Bruno Berselli, Table of n, a(n) for n = 1..1000 (First 211 terms from Vincenzo Librandi)
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: A146814 A034335 A337033 * A187257 A290186 A178703
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 31 2011
STATUS
approved