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 A161532 a(n) = 2n^2 + 8n + 1. 12
 1, 11, 25, 43, 65, 91, 121, 155, 193, 235, 281, 331, 385, 443, 505, 571, 641, 715, 793, 875, 961, 1051, 1145, 1243, 1345, 1451, 1561, 1675, 1793, 1915, 2041, 2171, 2305, 2443, 2585, 2731, 2881, 3035, 3193, 3355, 3521, 3691, 3865, 4043, 4225, 4411, 4601 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The defining formula can be regarded as an approximation and simplification of the expansion / propagation of native hydrophytes on the surface of stagnant waters in orthogonal directions; absence of competition / concurrence and of retrogression is assumed, mortality is taken into account. - [Translation of a comment in French sent by Pierre Gayet] Numbers of the form 2*n^2 - 7. - Boris Putievskiy, Feb 04 2013 LINKS Pierre Gayet, Table of n, a(n) for n = 0..10000 Pierre Gayet, Note et Compte rendu (gif version) Pierre Gayet, Note et Compte Rendu (pdf version) Claude Monet, Nymphéas Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = a(n-1) + 4*n + 6 (with a(0)=1). - Vincenzo Librandi, Nov 30 2010 G.f.: (1 + 8*x - 5*x^2)/(1 - x)^3. - Vincenzo Librandi, Feb 07 2013 MATHEMATICA Table[2*n^2+8*n+1, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jun 13 2009 *) CoefficientList[Series[(1 + 8*x - 5*x^2)/(1-x)^3, {x, 0, 60}], x] (* Vincenzo Librandi, Feb 07 2013 *) PROG (Magma) [ 2*n^2+8*n+1: n in [0..50] ]; (PARI) a(n)=2*n^2+8*n+1 \\ Charles R Greathouse IV, Jun 17 2017 CROSSREFS Cf. A161549, A161587, A161617, A161935, A162316. Sequence in context: A301635 A031025 A140675 * A328560 A118648 A262105 Adjacent sequences: A161529 A161530 A161531 * A161533 A161534 A161535 KEYWORD easy,nonn AUTHOR Pierre Gayet, Jun 13 2009 EXTENSIONS More terms from Vladimir Joseph Stephan Orlovsky, Jun 13 2009 STATUS approved

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Last modified December 2 17:17 EST 2022. Contains 358510 sequences. (Running on oeis4.)