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 A114203 #21 May 29 2024 16:23:39
%S A114203 1,2,4,8,18,44,110,272,662,1596,3838,9240,22286,53812,129974,313888,
%T A114203 757878,1829644,4416910,10662952,25742302,62147556,150038438,
%U A114203 362226480,874493446,2111213372,5096916094,12305037368,29706982638,71719002644,173145004310,418009044032
%N A114203 Row sums of a Pascal-Jacobsthal triangle.
%C A114203 Binomial transform of double Jacobsthal sequence 1,1,1,1,3,3,5,5,11,11,... Row sums of A114202.
%H A114203 Michael De Vlieger, <a href="/A114203/b114203.txt">Table of n, a(n) for n = 0..2613</a>
%H A114203 Sergio Falcón, <a href="https://www.rgnpublications.com/journals/index.php/cma/article/viewFile/1221/950">Binomial Transform of the Generalized k-Fibonacci Numbers</a>, Communications in Mathematics and Applications (2019) Vol. 10, No. 3, 643-651.
%H A114203 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2,2).
%F A114203 G.f.: (1-x)^2/((1 - 2*x - x^2)*(1 - 2*x + 2*x^2)).
%F A114203 a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) + 2*a(n-4).
%F A114203 a(n) = Sum_{k=0..n} Sum_{i=0..n-k} C(n-k, i)*C(k, i)*J(i).
%F A114203 a(n) = Sum_{k=0..n} C(n, k)*J(floor((k+2)/2)), J(n) = A001045(n).
%F A114203 E.g.f.: exp(x)*(cos(x) + 2*cosh(sqrt(2)*x) + sin(x) + sqrt(2)*sinh(sqrt(2)*x))/3. - _Stefano Spezia_, May 29 2024
%t A114203 LinearRecurrence[{4,-5,2,2},{1,2,4,8},40] (* _Harvey P. Dale_, Jun 05 2012 *)
%Y A114203 Cf. A001045, A114202.
%K A114203 easy,nonn
%O A114203 0,2
%A A114203 _Paul Barry_, Nov 16 2005