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 A203134 Decagonal hexagonal numbers 2
 1, 1540, 1777555, 2051297326, 2367195337045, 2731741367653000, 3152427171076225351, 3637898223680596402450, 4198131397700237172202345, 4844639995047850016125104076, 5590710356153821218371197901755, 6451674906361514638150346253521590 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS As n increases, this sequence is approximately geometric with common ratio (1+sqrt(2))^8 = 577+408*sqrt(2). LINKS Table of n, a(n) for n=1..12. Index entries for linear recurrences with constant coefficients, signature (1155, -1155, 1). FORMULA G.f.: x*(1+385*x+10*x^2) / ((1-x)*(1-1154*x+x^2)). a(n) = 1155*a(n-1)-1155*a(n-2)+a(n-3). a(n) = 1154*a(n-1)-a(n-2)+396. a(n) = (1/64)*((5*sqrt(2)-1)*(sqrt(2)+1)^(8*n-5)+ (5*sqrt(2)+1)*(sqrt(2)-1)^(8*n-5)-22). a(n) = floor(1/64 *(5*sqrt(2)-1)*(sqrt(2)+1)^(8*n-5)). EXAMPLE The second number which is both hexagonal and decagonal is 1540. Hence a(2) = 1540. MATHEMATICA LinearRecurrence[{1155, -1155, 1}, {1, 1540, 1777555}, 12] CROSSREFS Cf. A203135, A203136, A000384, A001107. Sequence in context: A237400 A200429 A092717 * A083734 A137598 A252966 Adjacent sequences: A203131 A203132 A203133 * A203135 A203136 A203137 KEYWORD nonn,easy AUTHOR Ant King, Dec 30 2011 STATUS approved

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Last modified July 18 21:02 EDT 2024. Contains 374388 sequences. (Running on oeis4.)