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 A100059 #20 Feb 07 2025 10:36:23
%S A100059 1,5,14,45,139,434,1351,4209,13110,40837,127203,396226,1234207,
%T A100059 3844441,11975078,37301261,116189979,361921042,1127350583,3511592833,
%U A100059 10938286998,34071752661,106130359315,330586256610
%N A100059 First differences of A052911.
%C A100059 a(n)/a(n-1) tends to 3.11490754148...an eigenvalue of M and a root of the characteristic polynomial x^3 - 3x^2 - x + 2.
%D A100059 Boris A. Bondarenko, Generalized Pascal Triangles and Pyramids (in Russian), FAN, Tashkent, 1990, ISBN 5-648-00738-8.
%H A100059 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,1,-2).
%H A100059 Boris A. Bondarenko, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/pascal.html">Generalized Pascal Triangles and Pyramids</a>, English translation published by Fibonacci Association, Santa Clara Univ., Santa Clara, CA, 1993; see p. 27.
%F A100059 G.f.: (2*x^2-2*x-1)*x / (-2*x^3+x^2+3*x-1).
%F A100059 Recurrence: a(n) = 3*a(n-1) + a(n-2) - 2*a(n-3).
%F A100059 a(n) = rightmost term in M^5 * [1 1 1], where M = the 3 X 3 upper triangular matrix [2 1 2 / 1 1 0 / 1 0 0].
%F A100059 INVERT transform of (1, 4, 5, 6, 7, 8, 9, ...) with offset 0.
%e A100059 a(5) = 139 = rightmost term in M^5 * [1 1 1] which is [434 205 139]. 434 = a(6), while 205 = A052911(5).
%e A100059 a(6) = 434 = 3*a(5) + a(4) - 2*a(3) = 3*139 + 45 - 2*14.
%t A100059 LinearRecurrence[{3,1,-2},{1,5,14},30] (* _Harvey P. Dale_, Apr 21 2016 *)
%Y A100059 Cf. A019481, A052550, A052939, A100058, A058071.
%K A100059 nonn
%O A100059 1,2
%A A100059 _Gary W. Adamson_, Oct 31 2004
%E A100059 Edited by _Ralf Stephan_, Nov 02 2004