# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a048910 Showing 1-1 of 1 %I A048910 #22 Aug 16 2015 12:03:56 %S A048910 1,2,18,49,529,1458,15842,43681,474721,1308962,14225778,39225169, %T A048910 426298609,1175446098,12774732482,35224157761,382815675841, %U A048910 1055549286722,11471695542738,31631254443889,343768050606289,947882084029938,10301569822645922,28404831266454241 %N A048910 Indices of 9-gonal numbers that are also square. %C A048910 From _Ant King_, Nov 18 2011: (Start) %C A048910 lim( n -> Infinity, a(2n+1)/a(2n)) = 1/25 * (137 + 36 * sqrt(14)) = 1/25 * (9 + 2 * sqrt(14))^2. %C A048910 lim( n -> Infinity, a(2n)/a(2n-1)) = 1/25 * (39 + 8 * sqrt(14)). %C A048910 (14 * a(n) - 5)^2 - 56 * A048911(n) ^ 2 = 25. %C A048910 (End) %H A048910 Colin Barker, Table of n, a(n) for n = 1..1000 %H A048910 Eric Weisstein's World of Mathematics, Nonagonal Square Number %H A048910 Index entries for linear recurrences with constant coefficients, signature (1,30,-30,-1,1). %F A048910 From _Ant King_, Nov 18 2011: (Start) %F A048910 a(n) = 30 * a(n - 2) - a(n-4) - 10. %F A048910 a(n) = a(n - 1) + 30 * a(n - 2) - 30 * a(n - 3) - a(n - 4) + a(n - 5). %F A048910 Let p = 9 + 4 * sqrt(2) + sqrt(7) + 2 * sqrt(14) and q = 9 - 4 * sqrt(2) - sqrt(7) + 2 * sqrt(14). Then %F A048910 a(n) = 1/56 * ( ( p - q * (-1) ^ n) * ( 2 * sqrt(2) + sqrt(7))^(n - 1) + ( p + q * (-1)^n) * ( 2 * sqrt(2) - sqrt(7))^n + 20 ). %F A048910 a(n) = ceiling (1/56 * ( p - q * (-1) ^ n) * ( 2 * sqrt(2) + sqrt(7))^(n - 1) ). %F A048910 G.f.: x * (1 + x - 14 * x^2 + x^3 + x^4) / ((1 - x) * (1 - 30 * x^2 + x^4)). %F A048910 (End) %t A048910 LinearRecurrence[ {1, 30, - 30, -1, 1 }, {1, 2, 18, 49, 529}, 21 ] (* _Ant King_, Nov 18 2011 *) %o A048910 (PARI) Vec(-x*(x^4+x^3-14*x^2+x+1)/((x-1)*(x^4-30*x^2+1)) + O(x^50)) \\ _Colin Barker_, Jun 22 2015 %Y A048910 Cf. A048911, A036411. %K A048910 nonn,easy %O A048910 1,2 %A A048910 _Eric W. Weisstein_ # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE