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 A377728 #39 Feb 03 2025 00:13:51
%S A377728 0,1,2,7,16,39,86,189,402,847,1760,3631,7438,15165,30794,62343,125904,
%T A377728 253783,510758,1026685,2061730,4136991,8295872,16627167,33311646,
%U A377728 66716029,133582106,267406999,535206832,1071049287,2143127030,4287918141,8578528818,17161414255
%N A377728 Convolution of Leonardo numbers with Jacobsthal numbers.
%H A377728 Prabha Sivaraman Nair, <a href="https://doi.org/10.20948/mathmontis-2024-61-3">Convolution Identities of p-numbers</a>, Math. Montis. (2024), pp. 26-43.
%H A377728 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-5,1,2).
%F A377728 a(n) = Sum_{i=0..n} L(i)*J(n-i) where L = A001595 and J = A001045.
%F A377728 a(n) = (3*J(n+2) - 2*L(n+1) - 1)/2 where L = A001595 and J = A001045.
%F A377728 G.f.: -x*(x^2-x+1)/((x-1)*(2*x-1)*(x+1)*(x^2+x-1)). - _Alois P. Heinz_, Nov 05 2024
%F A377728 E.g.f.: 2*cosh(2*x) + sinh(x) + 2*sinh(2*x) - 2*exp(x/2)*(5*cosh(sqrt(5)*x/2) + 3*sqrt(5)*sinh(sqrt(5)*x/2))/5. - _Stefano Spezia_, Nov 06 2024
%t A377728 LinearRecurrence[{3, 0, -5, 1, 2}, {0, 1, 2, 7, 16}, 34] (* _Amiram Eldar_, Nov 07 2024 *)
%o A377728 (Python)
%o A377728 from sympy import fibonacci
%o A377728 def A377728(n): return 1-(fibonacci(n+2)<<2)+(m:=(4<<n)+(1 if n&1 else -1))-m%3>>1 # _Chai Wah Wu_, Nov 09 2024
%Y A377728 Cf. A001045, A001595.
%K A377728 nonn,easy
%O A377728 0,3
%A A377728 _Prabha Sivaramannair_, Nov 05 2024