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 #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