A077261 Triangular numbers that are 5 times another triangular number.

0, 15, 105, 4950, 33930, 1594005, 10925475, 513264780, 3517969140, 165269665275, 1132775137725, 53216318953890, 364750076378430, 17135489433487425, 117448391818716855, 5517574381263997080, 37818017415550449000, 1776641815277573572455, 12177284159415425861265

Offset

0,2

Comments

The triangular numbers that are 1/5 are in A077260.

Links

Colin Barker, Table of n, a(n) for n = 0..797

Vladimir Pletser, Recurrent Relations for Multiple of Triangular Numbers being Triangular Numbers, arXiv:2101.00998 [math.NT], 2021.

Vladimir Pletser, Triangular Numbers Multiple of Triangular Numbers and Solutions of Pell Equations, arXiv:2102.13494 [math.NT], 2021.

Vladimir Pletser, Using Pell equation solutions to find all triangular numbers multiple of other triangular numbers, 2022.

Index entries for linear recurrences with constant coefficients, signature (1,322,-322,-1,1).

Formula

a(n) = 5*A077260(n).

G.f.: (-15*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

a(n) = 322*a(n-2) - a(n-4) + 120. - Vladimir Pletser, Feb 09 2021

Example

a(3)=5*990=4950.

Mathematica

CoefficientList[Series[(-15 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 *)

Crossrefs

Subsequence of A000217.

Cf. A077259, A077260, A077262.

Sequence in context: A344886 A165892 A349169 * A012507 A143727 A231327

Adjacent sequences: A077258 A077259 A077260 * A077262 A077263 A077264

Keyword

easy,nonn

Author

Bruce Corrigan (scentman(AT)myfamily.com), Nov 01 2002

Status

approved