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 A077260 Triangular numbers that are 1/5 of a triangular number. 12
 0, 3, 21, 990, 6786, 318801, 2185095, 102652956, 703593828, 33053933055, 226555027545, 10643263790778, 72950015275686, 3427097886697485, 23489678363743371, 1103514876252799416, 7563603483110089800, 355328363055514714491, 2435456831883085172253 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The triangular numbers 5x these are in A077261. 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) = 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 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 *) 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 Cf. A000217, A077259, A077261, A077262. Sequence in context: A111435 A111438 A058635 * A290766 A290872 A012110 Adjacent sequences: A077257 A077258 A077259 * A077261 A077262 A077263 KEYWORD easy,nonn AUTHOR Bruce Corrigan (scentman(AT)myfamily.com), Nov 01 2002 STATUS approved

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Last modified May 29 12:15 EDT 2023. Contains 363042 sequences. (Running on oeis4.)