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 A274603 Numbers n such that 2*n+1 and 3*n+1 are both triangular numbers. 5
 45, 4455, 436590, 42781410, 4192141635, 410787098865, 40252943547180, 3944377680524820, 386508759747885225, 37873914077612227275, 3711257070846250387770, 363665319028854925774230, 35635490007756936475486815, 3491914355441150919671933685 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Inspired by A274579. a(n+1) / a(n) goes to 49 + 20*sqrt(6) when n goes to infinity. Intersection of A045943 and A074377. - Colin Barker, Jun 30 2016 LINKS Colin Barker, Table of n, a(n) for n = 1..500 Index entries for linear recurrences with constant coefficients, signature (99,-99,1). FORMULA From Colin Barker, Jun 30 2016: (Start) a(n) = 99*a(n-1)-99*a(n-2)+a(n-3) for n>3. G.f.: 45*x / ((1-x)*(1-98*x+x^2)). (End) EXAMPLE 45 is a term because 2*45 + 1 = 91 and 3*45 + 1 = 136 are both triangular numbers. PROG (PARI) isok(n) = ispolygonal(2*n+1, 3) && ispolygonal(3*n+1, 3); (PARI) Vec(45*x/((1-x)*(1-98*x+x^2)) + O(x^20)) \\ Colin Barker, Jun 30 2016 CROSSREFS Cf. A000217, A045943, A074377, A274579. Sequence in context: A143004 A004707 A220094 * A036521 A328356 A093533 Adjacent sequences: A274600 A274601 A274602 * A274604 A274605 A274606 KEYWORD nonn,easy AUTHOR Altug Alkan, Jun 30 2016 EXTENSIONS More terms from Colin Barker, Jun 30 2016 STATUS approved

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Last modified June 24 09:41 EDT 2024. Contains 373674 sequences. (Running on oeis4.)