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 A022107 #23 Feb 18 2024 01:59:27
%S A022107 1,17,18,35,53,88,141,229,370,599,969,1568,2537,4105,6642,10747,17389,
%T A022107 28136,45525,73661,119186,192847,312033,504880,816913,1321793,2138706,
%U A022107 3460499,5599205,9059704,14658909
%N A022107 Fibonacci sequence beginning 1, 17.
%C A022107 a(n-1)=sum(P(17;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=16. These are the SW-NE diagonals in P(17;n,k), the (17,1) 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 A022107 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A022107 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1).
%F A022107 a(n)= a(n-1)+a(n-2), n>=2, a(0)=1, a(1)=17. a(-1):=16.
%F A022107 G.f.: (1+16*x)/(1-x-x^2).
%t A022107 a={};b=1;c=17;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 A022107 LinearRecurrence[{1,1},{1,17},40] (* _Harvey P. Dale_, Aug 04 2017 *)
%o A022107 (Magma) a0:=1; a1:=17; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..30]]; // _Bruno Berselli_, Feb 12 2013
%Y A022107 a(n) = A109754(16, n+1) = A101220(16, 0, n+1).
%K A022107 nonn,easy
%O A022107 0,2
%A A022107 _N. J. A. Sloane_