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A077261 Triangular numbers that are 5 times another triangular number. 11
0, 15, 105, 4950, 33930, 1594005, 10925475, 513264780, 3517969140, 165269665275, 1132775137725, 53216318953890, 364750076378430, 17135489433487425, 117448391818716855, 5517574381263997080, 37818017415550449000, 1776641815277573572455, 12177284159415425861265 (list; graph; refs; listen; history; text; internal format)
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.

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: A319588 A344886 A165892 * 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

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Last modified July 25 03:53 EDT 2021. Contains 346283 sequences. (Running on oeis4.)