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 A195021 a(n) = n*(14*n - 11). 9
 0, 3, 34, 93, 180, 295, 438, 609, 808, 1035, 1290, 1573, 1884, 2223, 2590, 2985, 3408, 3859, 4338, 4845, 5380, 5943, 6534, 7153, 7800, 8475, 9178, 9909, 10668, 11455, 12270, 13113, 13984, 14883, 15810, 16765, 17748, 18759, 19798, 20865, 21960, 23083 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Sequence found by reading the first two vertices [0, 3] together with the line from 34, in the direction 34, 93, ..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020, which is related to the primitive Pythagorean triple [3, 4, 5]. For another version see A195030. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = 14*n^2 - 11*n. From Colin Barker, Apr 09 2012: (Start) a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). G.f.: x*(3+25*x)/(1-x)^3. (End) PROG (MAGMA) [14*n^2 - 11*n: n in [0..50]]; // Vincenzo Librandi, Oct 14 2011 (PARI) a(n)=n*(14*n-11) \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Cf. A144555, A152760, A185019, A193053, A195019, A195020, A195023, A195024, A195025, A195030, A195320, A198017. Cf. numbers of the form n*(n*k-k+6))/2, this sequence is the case k=28: see Comments lines of A226492. Sequence in context: A003348 A344641 A086488 * A344429 A274871 A042041 Adjacent sequences:  A195018 A195019 A195020 * A195022 A195023 A195024 KEYWORD nonn,easy AUTHOR Omar E. Pol, Sep 07 2011 EXTENSIONS Edited by Bruno Berselli, Oct 18 2011 STATUS approved

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Last modified August 2 08:20 EDT 2021. Contains 346422 sequences. (Running on oeis4.)