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 A022392 #24 Feb 18 2024 02:01:04
%S A022392 1,22,23,45,68,113,181,294,475,769,1244,2013,3257,5270,8527,13797,
%T A022392 22324,36121,58445,94566,153011,247577,400588,648165,1048753,1696918,
%U A022392 2745671,4442589,7188260,11630849,18819109,30449958,49269067,79719025,128988092,208707117,337695209,546402326
%N A022392 Fibonacci sequence beginning 1, 22.
%C A022392 a(n-1) = Sum_{k=0..ceiling((n-1)/2)} P(22;n-1-k,k), n>=1, with a(-1)=21. These are the SW-NE diagonals in P(22;n,k), the (22,1) Pascal triangle. Cf. A093645 for the (10,1) Pascal triangle. Observation by _Paul Barry_, Apr 29 2004. Proof via recursion relations and comparison of inputs.
%H A022392 G. C. Greubel, <a href="/A022392/b022392.txt">Table of n, a(n) for n = 0..1000</a>
%H A022392 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A022392 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1).
%F A022392 a(n) = a(n-1) + a(n-2), n>=2, a(0)=1, a(1)=22. a(-1):=21.
%F A022392 G.f.: (1+21*x)/(1-x-x^2).
%t A022392 Table[Fibonacci[n + 2] + 20*Fibonacci[n], {n, 0, 50}] (* or *) LinearRecurrence[{1,1}, {1,22}, 50] (* _G. C. Greubel_, Mar 02 2018 *)
%o A022392 (PARI) for(n=0, 50, print1(fibonacci(n+2) + 20*fibonacci(n), ", ")) \\ _G. C. Greubel_, Mar 02 2018
%o A022392 (Magma) [Fibonacci(n+2) + 20*Fibonacci(n): n in [0..50]]; // _G. C. Greubel_, Mar 02 2018
%K A022392 nonn
%O A022392 0,2
%A A022392 _N. J. A. Sloane_
%E A022392 Terms a(30) onward added by _G. C. Greubel_, Mar 02 2018