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 A344109 #33 Aug 29 2025 11:08:13
%S A344109 4,1,9,11,29,51,109,211,429,851,1709,3411,6829,13651,27309,54611,
%T A344109 109229,218451,436909,873811,1747629,3495251,6990509,13981011,
%U A344109 27962029,55924051,111848109,223696211,447392429,894784851,1789569709,3579139411,7158278829,14316557651,28633115309,57266230611,114532461229,229064922451
%N A344109 a(n) = (5*2^n + 7*(-1)^n)/3.
%H A344109 Élis Gardel da Costa Mesquita, Eudes Antonio Costa, Paula M. M. C. Catarino, and Francisco R. V. Alves, <a href="https://doi.org/10.14244/lajm.v4i1.39">Jacobsthal-Mulatu Numbers</a>, Latin Amer. J. Math. (2025) Vol. 4, No. 1, 23-45. See pp. 24, 26, 43.
%H A344109 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,2).
%F A344109 a(n+1) = 5*2^n - a(n) for n >= 0, with a(0) = 4.
%F A344109 a(n+2) = 5*2^n + a(n) for n >= 0, with a(0) = 4, a(1) = 1.
%F A344109 a(n+3) = 15*2^n - a(n) for n >= 0, with a(0) = 4, a(1) = 1, a(2) = 9.
%F A344109 a(n) = A001045(n+2) + A154879(n).
%F A344109 a(2*n+1) = A321421(n).
%F A344109 a(n) = a(n-1) + 2*a(n-2) for n >= 2. - _Pontus von Brömssen_, May 09 2021
%F A344109 G.f.: (4 - 3*x)/(1 - x - 2*x^2). - _Stefano Spezia_, May 10 2021
%F A344109 a(n) = 2*A014551(n) - A001045(n).
%F A344109 a(n) = abs(A156550(n)) - (-1)^n.
%F A344109 a(n+3) = a(n) + 7*A084214(n+1) for n >= 0, with a(0) = 4.
%F A344109 a(n) = 5*A001045(n+1) - A084214(n+1) for n >= 0.
%F A344109 a(n) = A084214(n+1) + 3*(-1)^n for n >= 0.
%t A344109 LinearRecurrence[{1,2}, {4,1}, 28] (* _Amiram Eldar_, May 10 2021 *)
%Y A344109 Cf. A001045, A020714, A110286, A154879, A321421.
%Y A344109 Cf. A014551, A156550, A084214.
%K A344109 nonn,easy,changed
%O A344109 0,1
%A A344109 _Paul Curtz_, May 09 2021