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 A239794 5*n^2 + 4*n - 15. 1
 -6, 13, 42, 81, 130, 189, 258, 337, 426, 525, 634, 753, 882, 1021, 1170, 1329, 1498, 1677, 1866, 2065, 2274, 2493, 2722, 2961, 3210, 3469, 3738, 4017, 4306, 4605, 4914, 5233, 5562, 5901, 6250, 6609, 6978, 7357, 7746, 8145, 8554, 8973, 9402, 9841, 10290 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Follows the integer values from 1 on the quadratic equation 5*x^2 + 4*n - 15, this is the case x=n. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 WolframAlpha, Table of 5n^2+4n-15 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA From Bruno Berselli, Mar 27 2014: (Start) G.f.: -x*(6 - 31*x + 15*x^2)/(1 - x)^3. a(n+1) - a(n) = A017377(n). a(n) - a(-n) = A008590(n). (End) EXAMPLE For n=3, a(3) = 5*3^2 + 4*3 - 15 = 42; for n=6, a(6) = 5*6^2 + 4*6 - 15 = 189. MATHEMATICA Table[5 n^2 + 4 n - 15, {n, 50}] CoefficientList[Series[(6 - 31 x + 15 x^2)/(x - 1)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Mar 29 2014 *) PROG (Magma) [5*n^2+4*n-15: n in [1..50]]; (PARI) a(n)=5*n^2+4*n-15 \\ Charles R Greathouse IV, Jun 17 2017 CROSSREFS Cf. A008590, A017377. Sequence in context: A338267 A216508 A057451 * A034753 A100905 A353964 Adjacent sequences: A239791 A239792 A239793 * A239795 A239796 A239797 KEYWORD sign,easy AUTHOR Katherine Guo, Mar 26 2014 STATUS approved

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Last modified July 13 02:14 EDT 2024. Contains 374259 sequences. (Running on oeis4.)