This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A084150 #15 Oct 12 2022 09:03:02
%S A084150 0,0,1,3,14,50,199,749,2892,11028,42301,161799,619706,2372006,9081955,
%T A084150 34767953,133109592,509594856,1950956857,7469077707,28594853414,
%U A084150 109473250778,419110475455,1604533706357,6142840740900,23517417426300
%N A084150 A Pell related sequence.
%C A084150 Binomial transform of expansion of (sinh(sqrt(2)x))^2/4 = (0, 0, 1, 0, 8, 0, 64, ...). Inverse binomial transform of A006668.
%H A084150 G. C. Greubel, <a href="/A084150/b084150.txt">Table of n, a(n) for n = 0..1000</a>
%H A084150 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,5,-7).
%F A084150 a(n) = ( (1+sqrt(8))^n + (1-sqrt(8))^n - 2 )/16.
%F A084150 E.g.f.: (1/4)*exp(x)*( sinh(sqrt(2)*x) )^2.
%F A084150 G.f.: x^2 / ( (1-x)*(1-2*x-7*x^2) ). - _R. J. Mathar_, Feb 05 2011
%F A084150 a(n) = (A015519(n) - A015519(n-1) - 1)/8 = (A084058(n) - 1)/8. - _G. C. Greubel_, Oct 11 2022
%t A084150 LinearRecurrence[{3,5,-7}, {0,0,1}, 41] (* _G. C. Greubel_, Oct 11 2022 *)
%o A084150 (Magma) [n le 3 select Floor((n-1)/2) else 3*Self(n-1) +5*Self(n-2) -7*Self(n-3): n in [1..41]]; // _G. C. Greubel_, Oct 11 2022
%o A084150 (SageMath)
%o A084150 A084058 = BinaryRecurrenceSequence(2,7,1,1)
%o A084150 def A084150(n): return (A084058(n) - 1)/8
%o A084150 [A084150(n) for n in range(41)] # _G. C. Greubel_, Oct 11 2022
%Y A084150 Cf. A006646, A006668, A015519, A084058.
%K A084150 easy,nonn
%O A084150 0,4
%A A084150 _Paul Barry_, May 16 2003