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 A022108 #23 Feb 18 2024 01:59:31
%S A022108 1,18,19,37,56,93,149,242,391,633,1024,1657,2681,4338,7019,11357,
%T A022108 18376,29733,48109,77842,125951,203793,329744,533537,863281,1396818,
%U A022108 2260099,3656917,5917016,9573933,15490949
%N A022108 Fibonacci sequence beginning 1, 18.
%C A022108 a(n-1)=sum(P(18;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=17. These are the SW-NE diagonals in P(18;n,k), the (18,1) 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 A022108 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A022108 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1).
%F A022108 a(n)= a(n-1)+a(n-2), n>=2, a(0)=1, a(1)=18. a(-1):=17.
%F A022108 G.f.: (1+17*x)/(1-x-x^2).
%t A022108 a={};b=1;c=18;AppendTo[a,b];AppendTo[a,c];Do[b=b+c;AppendTo[a,b];c=b+c;AppendTo[a,c],{n,1,12,1}];a (* _Vladimir Joseph Stephan Orlovsky_, Jul 23 2008 *)
%t A022108 LinearRecurrence[{1,1},{1,18},40] (* _Harvey P. Dale_, Apr 15 2018 *)
%o A022108 (Magma) a0:=1; a1:=18; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..30]]; // _Bruno Berselli_, Feb 12 2013
%Y A022108 a(n) = A109754(17, n+1) = A101220(17, 0, n+1).
%K A022108 nonn,easy
%O A022108 0,2
%A A022108 _N. J. A. Sloane_