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 A110273 #15 Jan 20 2025 20:49:34
%S A110273 1,9,133,1853,26117,367389,5169809,72744121,1023588937,14402985777,
%T A110273 202665398173,2851718540021,40126725007181,564625868522949,
%U A110273 7944888884612393,111793070252410993,1573047872420021137,22134463284128711769,311455533850231631029,4382511937187348260781
%N A110273 a(n) = Pell(n)^3 + Pell(n+1)^3.
%H A110273 G. C. Greubel, <a href="/A110273/b110273.txt">Table of n, a(n) for n = 0..850</a>
%H A110273 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (12,30,-12,-1).
%F A110273 G.f.: (1+x)*(1-4*x-x^2)/((1+2*x-x^2)*(1-14*x-x^2)).
%F A110273 a(n) = 12*a(n-1) + 30*a(n-2) - 12*a(n-3) - a(n-4).
%F A110273 a(n) = ( 3*(-1)^n*A001333(n) + Pell(3*n) + Pell(3*(n+1)) )/8.
%t A110273 LinearRecurrence[{12,30,-12,-1},{1,9,133,1853},30] (* _Harvey P. Dale_, Jan 24 2018 *)
%t A110273 Sum[Fibonacci[Range[0, 30] +j, 2]^3, {j,0,1}] (* _G. C. Greubel_, Sep 17 2021 *)
%o A110273 (Magma) I:=[1,9,133,1853]; [n le 4 select I[n] else 12*Self(n-1) + 30*Self(n-2) - 12*Self(n-3) - Self(n-4): n in [1..31]]; // _G. C. Greubel_, Sep 17 2021
%o A110273 (Sage) [lucas_number1(n+1, 2, -1)^3 + lucas_number1(n, 2, -1)^3 for n in (0..30)] # _G. C. Greubel_, Sep 17 2021
%Y A110273 Cf. A000129, A110272.
%K A110273 easy,nonn
%O A110273 0,2
%A A110273 _Paul Barry_, Jul 18 2005