A160536 a(n) = Fibonacci(n) + n^2.
0, 2, 5, 11, 19, 30, 44, 62, 85, 115, 155, 210, 288, 402, 573, 835, 1243, 1886, 2908, 4542, 7165, 11387, 18195, 29186, 46944, 75650, 122069, 197147, 318595, 515070, 832940, 1347230, 2179333, 3525667, 5704043, 9228690, 14931648, 24159186, 39089613, 63247507
Offset: 0
Examples
a(6) = Fibonacci(6) + 6^2 = 8 + 36 = 44.
Links
- Bruno Berselli, Table of n, a(n) for n = 0..1000 (terms 0..285 from Vincenzo Librandi).
- Math Marathon (MM95) (In Russian) [Vladimir Joseph Stephan Orlovsky, May 12 2010]
- Index entries for linear recurrences with constant coefficients, signature (4,-5,1,2,-1).
Programs
-
Magma
[ Fibonacci(n)+n^2: n in [0..40] ]; // Klaus Brockhaus, May 22 2009
-
Mathematica
Table[Fibonacci[n]+n^2,{n,0,5!}] (* Vladimir Joseph Stephan Orlovsky, May 12 2010 *) -
PARI
a(n)=fibonacci(n)+n^2 \\ Charles R Greathouse IV, Oct 07 2015
Formula
a(n) = a(n-4) - a(n-3) - 2*a(n-2) + 3*a(n-1) - 2 for n > 3; a(0)=0, a(1)=2, a(2)=5, a(3)=11. - Klaus Brockhaus, May 22 2009
G.f.: x*(2-3*x+x^2-2*x^3) / ((1-x)^3*(1-x-x^2)). - Klaus Brockhaus, May 22 2009
Extensions
Edited and extended by Klaus Brockhaus, May 22 2009