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 A251793 Numbers n such that the sum of the triangular numbers T(n) and T(n+1) is equal to the sum of the octagonal numbers N(m) and N(m+1) for some m. 2
 0, 2, 68, 286, 6760, 28122, 662508, 2755766, 64919120, 270037042, 6361411348, 26460874446, 623353393080, 2592895658762, 61082271110588, 254077313684326, 5985439215444640, 24896983845405282, 586511960842464228, 2439650339536033406 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also nonnegative integers y in the solutions to 6*x^2-y^2+2*x-2*y = 0, the corresponding values of x being A220755. LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,98,-98,-1,1). FORMULA a(n) = a(n-1)+98*a(n-2)-98*a(n-3)-a(n-4)+a(n-5). G.f.: -2*x^2*(3*x^3+11*x^2+33*x+1) / ((x-1)*(x^2-10*x+1)*(x^2+10*x+1)). EXAMPLE 68 is in the sequence because T(68)+T(69) = 2346+2415 = 4761 = 2296+2465 = N(28)+N(29). PROG (PARI) concat(0, Vec(-2*x^2*(3*x^3+11*x^2+33*x+1)/((x-1)*(x^2-10*x+1)*(x^2+10*x+1)) + O(x^100))) CROSSREFS Cf. A000217, A000567, A220755. Sequence in context: A191808 A202606 A304044 * A283038 A264457 A246744 Adjacent sequences:  A251790 A251791 A251792 * A251794 A251795 A251796 KEYWORD nonn,easy AUTHOR Colin Barker, Dec 09 2014 STATUS approved

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Last modified November 29 15:46 EST 2021. Contains 349416 sequences. (Running on oeis4.)