Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #14 Aug 27 2022 08:14:30
%S 4,14,40,96,222,488,1052,2222,4640,9592,19694,40208,81748,165646,
%T 334776,675184,1359486,2733720,5491308,11021230,22104944,44310984,
%U 88785550,177835776,356099812,712892558,1426906312,2855626752,5714188830,11433127112,22873939004
%N a(n) = a(n-1) + 2*a(n-2) + 8*Fibonacci(n) + 2*Fibonacci(n-1); a(1) = 4, a(2) = 14.
%H Robert Israel, <a href="/A291675/b291675.txt">Table of n, a(n) for n = 1..3315</a>
%H J. Nilsson, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL20/Nilsson/nilsson15.html">On Counting the Number of Tilings of a Rectangle with Squares of Size 1 and 2</a>, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.2. [Page 10, Lemma 5]
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-3,-2).
%F G.f.: 2*x*(2*x^2+3*x+2)/((2*x-1)*(x+1)*(x^2+x-1)). - _Robert Israel_, Aug 29 2017
%p f:= gfun:-rectoproc({2*a(n)+3*a(n+1)-2*a(n+2)-2*a(n+3)+a(n+4), a(0) = 0, a(1) = 4, a(2) = 14, a(3) = 40},a(n),remember):
%p map(f, [$1..100]); # _Robert Israel_, Aug 29 2017
%t LinearRecurrence[{2, 2, -3, -2}, {4, 14, 40, 96}, 31] (* _Jean-François Alcover_, Aug 27 2022 *)
%K nonn
%O 1,1
%A _Eric M. Schmidt_, Aug 29 2017