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 A341895 #41 Oct 07 2022 10:14:30
%S A341895 0,4,20,39,175,779,1500,6664,29600,56979,253075,1124039,2163720,
%T A341895 9610204,42683900,82164399,364934695,1620864179,3120083460,
%U A341895 13857908224,61550154920,118481007099,526235577835,2337285022799,4499158186320,19983094049524,88755280711460,170849530073079,758831338304095,3370363382012699
%N A341895 Indices of triangular numbers that are ten times other triangular numbers.
%C A341895 Second member of the Diophantine pair (b(n), a(n)) that satisfies a(n)^2 + a(n) = 10*(b(n)^2 + b(n)) or T(a(n)) = 10*T(b(n)) where T(x) is the triangular number of x. The T(b)'s are in A068085 and the b's are in A341893.
%C A341895 Can be defined for negative n by setting a(-n) = -a(n+1) - 1 for all n in Z.
%H A341895 Vladimir Pletser, <a href="/A341895/b341895.txt">Table of n, a(n) for n = 1..1000</a>
%H A341895 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 A341895 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,38,-38,-1,1).
%F A341895 a(n) = 38*a(n-3) - a(n-6) + 18 for n > 3, with a(-2) = -21, a(-1) = -5, a(0) = -1, a(1) = 0, a(2) = 4, a(3) = 20.
%F A341895 a(n) = a(n-1) + 38*(a(n-3) - a(n-4)) - (a(n-6) - a(n-7)) for n >= 4 with a(-2) = -21, a(-1) = -5, a(0) = -1, a(1) = 0, a(2) = 4, a(3) = 20.
%F A341895 G.f.: x^2*(4 + 16*x + 19*x^2 - 16*x^3 - 4*x^4 - x^5)/(1 - x - 38*x^3 + 38*x^4 + x^6 - x^7). - _Stefano Spezia_, Feb 24 2021
%F A341895 a(n) = (A198943(n) + 1)/2 - 1. - _Hugo Pfoertner_, Feb 26 2021
%e A341895 a(2) = 4 is a term because its triangular number, T(a(2)) = 4*5 / 2 = 10 is ten times a triangular number.
%e A341895 a(4) = 38*a(1) - a(-2) + 18 = 38*0 - (-21) + 18 = 39, etc.
%p A341895 f := gfun:-rectoproc({a(-2) = -21, a(-1) = -5, a(0) = -1, a(1) = 0, a(2) = 4, a(3) = 20, a(n) = 38*a(n-3)-a(n-6)+18}, a(n), remember); map(f, [`$`(0 .. 1000)]) ; #
%t A341895 Rest@ CoefficientList[Series[x^2*(4 + 16*x + 19*x^2 - 16*x^3 - 4*x^4 - x^5)/(1 - x - 38*x^3 + 38*x^4 + x^6 - x^7), {x, 0, 30}], x] (* _Michael De Vlieger_, May 19 2022 *)
%Y A341895 Cf. A341893, A068085, A166477 (n=10).
%Y A341895 Cf. A336623, A336624, A336626, A336625, A053141, A001652, A075528, A029549, A061278, A001571, A076139, A076140, A077259, A077262, A077260, A077261, A077288, A077291, A077289, A077290, A077398, A077401, A077399, A077400, A000217.
%K A341895 easy,nonn
%O A341895 1,2
%A A341895 _Vladimir Pletser_, Feb 23 2021