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 A077260 #42 Aug 16 2024 04:48:27
%S A077260 0,3,21,990,6786,318801,2185095,102652956,703593828,33053933055,
%T A077260 226555027545,10643263790778,72950015275686,3427097886697485,
%U A077260 23489678363743371,1103514876252799416,7563603483110089800,355328363055514714491,2435456831883085172253,114414629388999485266710
%N A077260 Triangular numbers that are 1/5 of a triangular number.
%H A077260 Colin Barker, <a href="/A077260/b077260.txt">Table of n, a(n) for n = 0..798</a>
%H A077260 Vladimir Pletser, <a href="https://arxiv.org/abs/2101.00998">Recurrent Relations for Multiple of Triangular Numbers being Triangular Numbers</a>, arXiv:2101.00998 [math.NT], 2021.
%H A077260 Vladimir Pletser, <a href="https://arxiv.org/abs/2102.13494">Triangular Numbers Multiple of Triangular Numbers and Solutions of Pell Equations</a>, arXiv:2102.13494 [math.NT], 2021.
%H A077260 Vladimir Pletser, <a href="https://www.researchgate.net/profile/Vladimir-Pletser/publication/359808848_USING_PELL_EQUATION_SOLUTIONS_TO_FIND_ALL_TRIANGULAR_NUMBERS_MULTIPLE_OF_OTHER_TRIANGULAR_NUMBERS/">Using Pell equation solutions to find all triangular numbers multiple of other triangular numbers</a>, 2022.
%H A077260 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,322,-322,-1,1).
%F A077260 a(n) = A077261(n)/5.
%F A077260 a(n) = b(n)*(b(n)+1)/2 where b(n) = A077259(n).
%F A077260 a(n) = (A000045(A007310(n+1))^2-1)/8. - _Vladeta Jovovic_, Nov 02 2002. - Definition corrected by _R. J. Mathar_, Sep 16 2009
%F A077260 G.f.: (-3*x*(x^2+6*x+1))/((x-1)*(x^2-18*x+1)*(x^2+18*x+1)). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009
%F A077260 a(n) = 322*a(n-2) - a(n-4) + 24. - _Vladimir Pletser_, Mar 23 2020
%F A077260 E.g.f.: (-6*cosh(x) - (-3 + sqrt(5))*cosh((9 - 4*sqrt(5))*x) + (3 + sqrt(5))*cosh((9 + 4*sqrt(5))*x) - 6*sinh(x) + (7 - 3*sqrt(5))*sinh((9 - 4*sqrt(5))*x) + (7 + 3*sqrt(5))*sinh((9 + 4*sqrt(5))*x))/80. - _Stefano Spezia_, Aug 15 2024
%e A077260 Since b(3)=44 -> a(3)=44*45/2=990.
%t A077260 CoefficientList[Series[(-3 x (x^2 + 6 x + 1))/((x - 1) (x^2 - 18 x + 1)*(x^2 + 18 x + 1)), {x, 0, 18}], x] (* _Michael De Vlieger_, Apr 21 2021 *)
%t A077260 LinearRecurrence[{1,322,-322,-1,1},{0,3,21,990,6786},20] (* _Harvey P. Dale_, Dec 12 2023 *)
%o A077260 (PARI) concat(0, Vec(-3*x*(x^2+6*x+1) / ((x-1)*(x^2-18*x+1)*(x^2+18*x+1)) + O(x^100))) \\ _Colin Barker_, May 15 2015
%Y A077260 Cf. A000217, A077259, A077261, A077262.
%K A077260 easy,nonn
%O A077260 0,2
%A A077260 Bruce Corrigan (scentman(AT)myfamily.com), Nov 01 2002