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 A046192 Octagonal hexagonal numbers. 3
 1, 11781, 113123361, 1086210502741, 10429793134197921, 100146872588357936901, 961610260163619775927681, 9233381617944204500099658261, 88658929333889991446337142696641, 851303030230630079923524744073490821, 8174211607615580693535693146256516168801, 78488779005021775588699645666830324179338581 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS As n increases, this sequence is approximately geometric with common ratio r = lim_{n->infinity} a(n)/a(n-1) = (sqrt(3) + sqrt(2))^8 = 4801 + 1960*sqrt(6). - Ant King, Dec 27 2011 Intersection of A000384 and A000567. - Michel Marcus, Jun 20 2015 LINKS Herman Jamke, Table of n, a(n) for n = 1..20 Eric Weisstein's World of Mathematics, Octagonal Hexagonal Number. Index entries for linear recurrences with constant coefficients, signature (9603,-9603,1). FORMULA From Ant King, Dec 27 2011: (Start) G.f.: x*(1 + 2178*x + 21*x^2)/((1-x)*(1 - 9602*x + x^2)). a(n) = 9603*a(n-1) - 9603*a(n-2) + a(n-3). a(n) = 9602*a(n-1) - a(n-2) + 2200. a(n) = 1/96*((3*sqrt(3) - sqrt(2))*(sqrt(3) + sqrt(2))^(8n-5)+ (3*sqrt(3) + sqrt(2))*(sqrt(3) - sqrt(2))^(8n-5) - 22). a(n) = floor(1/96*(3*sqrt(3) - sqrt(2))*(sqrt(3) + sqrt(2))^(8n-5)). (End) MAPLE a:=5+2*sqrt(6): b:=5-2*sqrt(6): s:=n->a^n+b^n: d:=n->sqrt(6)*(a^n-b^n):for n from 0 to 40 do x:=simplify(s(n)-1/4*d(n)): y:=simplify(1/3*d(n)-s(n)/2): if(type((1+x/2)/3, integer) and type((1+y)/4, integer)) then printf("%d, ", (y^2-1)/8) fi: x:=simplify(s(n+1)+1/4*d(n+1)): y:=simplify(1/3*d(n+1)+s(n+1)/2): if(type((1+x/2)/3, integer) and type((1+y)/4, integer)) then printf("%d, ", (y^2-1)/8) fi: od: # Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 19 2008 MATHEMATICA LinearRecurrence[{9603, -9603, 1}, {1, 11781, 113123361}, 9] (* Ant King, Dec 27 2011 *) CoefficientList[Series[(1 + 2178 x + 21 x^2) / ((1 - x) (1 - 9602 x + x^2)), {x, 0, 33}], x] (* Vincenzo Librandi, Aug 10 2017 *) PROG (MAGMA) I:=[1, 11781, 113123361]; [n le 3 select I[n] else 9603*Self(n-1)-9603*Self(n-2)+Self(n-3): n in [1..30]]; // Vincenzo Librandi, Aug 10 2017 CROSSREFS Cf. A046190, A046191. Sequence in context: A229411 A235316 A321158 * A210151 A278193 A031868 Adjacent sequences:  A046189 A046190 A046191 * A046193 A046194 A046195 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Larry Reeves (larryr(AT)acm.org), May 07 2001 One more term from Lior Manor, Feb 13 2002 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 19 2008 STATUS approved

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Last modified December 9 19:48 EST 2018. Contains 318023 sequences. (Running on oeis4.)