OFFSET
0,2
LINKS
Colin Barker, Table of n, a(n) for n = 0..798
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) = A077261(n)/5.
a(n) = b(n)*(b(n)+1)/2 where b(n) = A077259(n).
a(n) = (A000045(A007310(n+1))^2-1)/8. - Vladeta Jovovic, Nov 02 2002. - Definition corrected by R. J. Mathar, Sep 16 2009
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
a(n) = 322*a(n-2) - a(n-4) + 24. - Vladimir Pletser, Mar 23 2020
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
EXAMPLE
Since b(3)=44 -> a(3)=44*45/2=990.
MATHEMATICA
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 *)
LinearRecurrence[{1, 322, -322, -1, 1}, {0, 3, 21, 990, 6786}, 20] (* Harvey P. Dale, Dec 12 2023 *)
PROG
(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
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Bruce Corrigan (scentman(AT)myfamily.com), Nov 01 2002
STATUS
approved