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 A371596 #16 Apr 13 2024 23:02:41
%S A371596 1,4,8,20,48,116,280,676,1632,3940,9512,22964,55440,133844,323128,
%T A371596 780100,1883328,4546756,10976840,26500436,63977712,154455860,
%U A371596 372889432,900234724,2173358880,5246952484,12667263848,30581480180,73830224208,178241928596,430314081400
%N A371596 The number of unilevel points (unique points at their height) on Delannoy paths ending when x = n.
%H A371596 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,1).
%F A371596 G.f.: (1 + 2*x - x^2)/(1 - 2*x - x^2).
%F A371596 a(n) = 4 * A000129(n) for n >= 1.
%e A371596 There are 5 paths ending with x=2. Of these, UU has 3 unilevel points, UD has 1, L has none, DU has 1, and DD has 3.
%t A371596 CoefficientList[Series[(1+2*x-x^2)/(1-2*x-x^2),{x,0,24}],x]
%Y A371596 Cf. A000129, A008288.
%K A371596 nonn,easy
%O A371596 0,2
%A A371596 _Lou Shapiro_, Mar 28 2024