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 A238375 #16 May 23 2021 02:53:04
%S A238375 1,2,4,6,11,16,28,40,69,98,168,238,407,576,984,1392,2377,3362,5740,
%T A238375 8118,13859,19600,33460,47320,80781,114242,195024,275806,470831,
%U A238375 665856,1136688,1607520,2744209,3880898,6625108,9369318,15994427,22619536,38613964,54608392
%N A238375 Row sums of triangle in A152719.
%H A238375 G. C. Greubel, <a href="/A238375/b238375.txt">Table of n, a(n) for n = 0..1000</a>
%H A238375 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,1,-1).
%F A238375 a(n) = Sum_{k=0..n} A152719(n,k).
%F A238375 G.f.: (1+x)/((1-2*x^2-x^4)*(1-x)).
%F A238375 a(2*n) = A005409(n+2).
%F A238375 a(2*n+1) = 2*A048739(n).
%F A238375 a(n) = (-4 + 2*(1+(-1)^n)*Pell((n+4)/2) + (1-(-1)^n)*Q((n+3)/2))/4, where Pell(n) = A000129(n) and Q(n) = A002203(n). - _G. C. Greubel_, May 21 2021
%F A238375 a(n) = a(n-1)+2*a(n-2)-2*a(n-3)+a(n-4)-a(n-5). - _Wesley Ivan Hurt_, May 22 2021
%e A238375 Triangle A152719 and row sums:
%e A238375 1; ............................. sum = 1
%e A238375 1, 1; .......................... sum = 2
%e A238375 1, 2, 1; ....................... sum = 4
%e A238375 1, 2, 2, 1; ................... sum = 6
%e A238375 1, 2, 5, 2, 1; ............... sum = 11
%e A238375 1, 2, 5, 5, 2, 1; ............ sum = 16
%e A238375 1, 2, 5, 12, 5, 2, 1; ......... sum = 28
%e A238375 1, 2, 5, 12, 12, 5, 2, 1; ...... sum = 40
%t A238375 Table[Sum[Fibonacci[1+Min[k, n-k], 2], {k,0,n}], {n,0,45}] (* _G. C. Greubel_, May 21 2021 *)
%o A238375 (Sage)
%o A238375 def Pell(n): return n if (n<2) else 2*Pell(n-1) + Pell(n-2)
%o A238375 def a(n): return sum(Pell(1+min(k, n-k)) for k in (0..n))
%o A238375 [a(n) for n in (0..45)] # _G. C. Greubel_, May 21 2021
%o A238375 (PARI) my(x='x+O('x^44)); Vec((1+x)/((1-2*x^2-x^4)*(1-x))) \\ _Joerg Arndt_, May 22 2021
%Y A238375 Cf. A000129, A002203, A005409, A048739, A135153 (first differences), A152719.
%K A238375 easy,nonn
%O A238375 0,2
%A A238375 _Philippe Deléham_, Feb 25 2014