%I #27 Oct 06 2024 18:14:34
%S 0,2,5,11,19,30,44,62,85,115,155,210,288,402,573,835,1243,1886,2908,
%T 4542,7165,11387,18195,29186,46944,75650,122069,197147,318595,515070,
%U 832940,1347230,2179333,3525667,5704043,9228690,14931648,24159186,39089613,63247507
%N a(n) = Fibonacci(n) + n^2.
%H Bruno Berselli, <a href="/A160536/b160536.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..285 from Vincenzo Librandi).
%H <a href="http://dxdy.ru/topic16091.html">Math Marathon (MM95)</a> (In Russian) [Vladimir Joseph Stephan Orlovsky, May 12 2010]
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,1,2,-1).
%F 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
%F G.f.: x*(2-3*x+x^2-2*x^3) / ((1-x)^3*(1-x-x^2)). - _Klaus Brockhaus_, May 22 2009
%e a(6) = Fibonacci(6) + 6^2 = 8 + 36 = 44.
%t Table[Fibonacci[n]+n^2,{n,0,5!}] (* _Vladimir Joseph Stephan Orlovsky_, May 12 2010 *)
%o (Magma) [ Fibonacci(n)+n^2: n in [0..40] ]; // _Klaus Brockhaus_, May 22 2009
%o (PARI) a(n)=fibonacci(n)+n^2 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Equals A000045 + A000290.
%Y Cf. A001611, A002062, A212272.
%K nonn,easy
%O 0,2
%A _Leonardo Sznajder_, May 18 2009
%E Edited and extended by _Klaus Brockhaus_, May 22 2009