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%I #23 Aug 18 2023 17:03:01
%S 1,3,10,42,199,981,4888,24420,122077,610359,3051766,15258798,76293955,
%T 381469737,1907348644,9536743176,47683715833,238418579115,
%U 1192092895522,5960464477554,29802322387711,149011611938493,745058059692400,3725290298461932,18626451492309589
%N Expansion of g.f.: (1-4*x)/((1-5*x)*(1-x)^2).
%C An approximation to A091843.
%H G. C. Greubel, <a href="/A094195/b094195.txt">Table of n, a(n) for n = 0..1000</a>
%H F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">A Slow-Growing Sequence Defined by an Unusual Recurrence</a>, J. Integer Sequences, Vol. 10 (2007), #07.1.2.
%H F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence [<a href="http://neilsloane.com/doc/gijs.pdf">pdf</a>, <a href="http://neilsloane.com/doc/gijs.ps">ps</a>].
%H <a href="/index/Ge#Gijswijt">Index entries for sequences related to Gijswijt's sequence</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-11,5).
%F a(n) = (5^(n+1) + 12*n + 11)/16.
%F a(n) = 7*a(n-1) - 11*a(n-2) + 5*a(n-3), with a(0)=1, a(1)=3, a(2)=10. - _Harvey P. Dale_, Dec 31 2011
%F E.g.f.: (1/16)*(5*exp(5*x) + (11 + 12*x)*exp(x)). - _G. C. Greubel_, Aug 18 2023
%t CoefficientList[Series[(1-4x)/((1-5x)(1-x)^2),{x,0,30}],x] (* or *) LinearRecurrence[{7,-11,5},{1,3,10},30] (* _Harvey P. Dale_, Dec 31 2011 *)
%o (Magma) [(5^(n+1) +12*n +11)/16: n in [0..40]]; // _G. C. Greubel_, Aug 18 2023
%o (SageMath) [(5^(n+1) +12*n +11)/16 for n in range(41)] # _G. C. Greubel_, Aug 18 2023
%Y Cf. A047926, A073724, A090822, A091843.
%Y A row of A094250.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Jun 01 2004
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