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 A167499 a(n) = n*(n+3)/2 + 6. 9
 6, 8, 11, 15, 20, 26, 33, 41, 50, 60, 71, 83, 96, 110, 125, 141, 158, 176, 195, 215, 236, 258, 281, 305, 330, 356, 383, 411, 440, 470, 501, 533, 566, 600, 635, 671, 708, 746, 785, 825, 866, 908, 951, 995, 1040, 1086, 1133, 1181, 1230, 1280, 1331, 1383, 1436, 1490 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Numbers m > 5 such that 8*m - 39 is a square. - Bruce J. Nicholson, Jul 25 2017 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Ângela Mestre and José Agapito, Square Matrices Generated by Sequences of Riordan Arrays, J. Int. Seq., Vol. 22 (2019), Article 19.8.4. Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = n + a(n-1) + 1, with n > 1, a(1) = 8. G.f.: (6 - 10*x + 5*x^2)/(1-x)^3. - Vincenzo Librandi, Sep 16 2013 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Sep 16 2013 Sum_{n>=0} 1/a(n) = 2*Pi*tanh(Pi*sqrt(39)/2)/sqrt(39) - 1/5. - Amiram Eldar, Jan 17 2021 MAPLE A167499:=n->n*(n+3)/2+6: seq(A167499(n), n=0..100); # Wesley Ivan Hurt, Jul 25 2017 MATHEMATICA Table[n*(n + 3)/2 + 6, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jun 03 2011 *) CoefficientList[Series[(6 - 10 x + 5 x^2) / (1 - x)^3, {x, 0, 60}], x] (* Vincenzo Librandi, Sep 16 2013 *) LinearRecurrence[{3, -3, 1}, {6, 8, 11}, 60] (* Harvey P. Dale, Jun 21 2022 *) PROG (Magma) [n*(n+3)/2+6: n in [0..60]]; // Vincenzo Librandi, Sep 16 2013 (PARI) a(n)=n*(n+3)/2+6 \\ Charles R Greathouse IV, Jun 17 2017 CROSSREFS Sequence in context: A315855 A287408 A287398 * A020716 A020937 A183208 Adjacent sequences: A167496 A167497 A167498 * A167500 A167501 A167502 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Nov 07 2009 STATUS approved

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Last modified November 27 19:48 EST 2022. Contains 358406 sequences. (Running on oeis4.)