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%I M0844 N0319 #65 Aug 03 2023 01:42:28
%S 0,2,3,7,15,34,78,182,429,1019,2433,5830,14004,33694,81159,195635,
%T 471819,1138286,2746794,6629290,16001193,38624911,93240069,225087338,
%U 543386088,1311813146,3166937355,7645566463,18457873863,44560996378,107579352390,259718869118
%N Sum of Fibonacci (A000045) and Pell (A000129) numbers.
%C In general, the sum of two Horadam sequences having signatures of (a,b) and (c,d) will be a fourth-order sequence with signature (a+c,d-a*c+b,-a*d-b*c,-b*d). - _Gary Detlefs_, Oct 13 2020
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A001932/b001932.txt">Table of n, a(n) for n = 0..501</a>
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HoradamSequence.html">Horadam Sequence</a>.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-3,-1).
%p gfpell := x/(1-2*x-x^2): gffib := x/(1-x-x^2): s := series(gfpell+gffib, x, 100): for i from 1 to 60 do printf(`%d,`,coeff(s,x,i)) od:
%p A001932:=-(z+2)*(2*z-1)/(z**2+z-1)/(z**2+2*z-1); # Conjectured (correctly) by _Simon Plouffe_ in his 1992 dissertation
%p with (combinat):seq(sum((fibonacci(n,m)),m=1..2),n=1..30); # _Zerinvary Lajos_, Jun 19 2008
%t nn = 30; CoefficientList[Series[-x*(x + 2)*(2*x - 1)/(x^2 + x - 1)/(x^2 + 2*x - 1), {x, 0, nn}], x] (* _T. D. Noe_, Aug 17 2012 *)
%t LinearRecurrence[{3, 0, -3, -1}, {0, 2, 3, 7}, 30] (* _T. D. Noe_, Apr 16 2013 *)
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _James A. Sellers_, Apr 06 2001
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