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 A087125 Indices n of hex numbers H(n) that are also triangular. 2
 0, 5, 54, 539, 5340, 52865, 523314, 5180279, 51279480, 507614525, 5024865774, 49741043219, 492385566420, 4874114620985, 48248760643434, 477613491813359, 4727886157490160, 46801248083088245, 463284594673392294, 4586044698650834699, 45397162391834954700 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Editors, L'Intermédiaire des Mathématiciens, Query 4500: The equation x(x+1)/2 = y*(y+1)/3, L'Intermédiaire des Mathématiciens, 22 (1915), 255-260 (I). Editors, L'Intermédiaire des Mathématiciens, Query 4500: The equation x(x+1)/2 = y*(y+1)/3, L'Intermédiaire des Mathématiciens, 22 (1915), 255-260 (II). Editors, L'Intermédiaire des Mathématiciens, Query 4500: The equation x(x+1)/2 = y*(y+1)/3, L'Intermédiaire des Mathématiciens, 22 (1915), 255-260 (III). Editors, L'Intermédiaire des Mathématiciens, Query 4500: The equation x(x+1)/2 = y*(y+1)/3, L'Intermédiaire des Mathématiciens, 22 (1915), 255-260 (IV). Eric Weisstein's World of Mathematics, Hex Number Index entries for linear recurrences with constant coefficients, signature (11,-11,1). FORMULA G.f.: (-x^2+5*x)/((1-x)*(1-10*x+x^2)). a(n) = 11*a(n-1)-11*a(n-2)+a(n-3) for n>2. - Colin Barker, Jun 23 2015 a(n) = (-4-(5-2*sqrt(6))^n*(-2+sqrt(6))+(2+sqrt(6))*(5+2*sqrt(6))^n)/8. - Colin Barker, Mar 05 2016 MATHEMATICA CoefficientList[Series[(-x^2+5*x)/((1-x)*(1-10*x+x^2)), {x, 0, 25}], x] (* G. C. Greubel, Nov 04 2017 *) LinearRecurrence[{11, -11, 1}, {0, 5, 54}, 30] (* Harvey P. Dale, Jun 14 2022 *) PROG (PARI) concat(0, Vec(x*(x-5)/((x-1)*(x^2-10*x+1)) + O(x^50))) \\ Colin Barker, Jun 23 2015 (Magma) [Round((-4-(5-2*Sqrt(6))^n*(-2+Sqrt(6)) + (2+Sqrt(6))*(5 + 2*Sqrt(6))^n)/8): n in [0..25]]; // G. C. Greubel, Nov 04 2017 CROSSREFS Cf. A006244, A031138. Sequence in context: A221544 A268882 A229298 * A110430 A110432 A215542 Adjacent sequences: A087122 A087123 A087124 * A087126 A087127 A087128 KEYWORD nonn,easy AUTHOR Eric W. Weisstein, Aug 14 2003 STATUS approved

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Last modified February 5 14:24 EST 2023. Contains 360086 sequences. (Running on oeis4.)