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 A203135 Indices of hexagonal numbers that are also decagonal 2
 1, 28, 943, 32026, 1087933, 36957688, 1255473451, 42649139638, 1448815274233, 49217070184276, 1671931570991143, 56796456343514578, 1929407584108504501, 65543061403345638448, 2226534680129643202723, 75636636063004523254126, 2569419091462024147437553 (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))^4=17+12*sqrt(2). LINKS Table of n, a(n) for n=1..17. Index entries for linear recurrences with constant coefficients, signature (35, -35, 1). FORMULA G.f.: x(1-7*x-2*x^2) / ((1-x)*(1-34*x+x^2)) a(n) = 35*a(n-1)-35*a(n-2)+a(n-3) a(n) = 34*a(n-1)-a(n-2)-8 a(n) = 1/16 *((3*sqrt(2)-2)*(1+sqrt(2))^(4*n-2)- (3*sqrt(2)+2)*(1-sqrt(2))^(4*n-2)+4) a(n) = ceiling(1/16 *(3*sqrt(2)-2)*(1+sqrt(2))^(4*n-2)) EXAMPLE The second hexagonal number which is also decagonal is A000384(28)=1540. Hence a(2) = 28. MATHEMATICA LinearRecurrence[{35, -35, 1}, {1, 28, 943}, 17] CROSSREFS Cf. A203134, A203136, A000384, A001107. Sequence in context: A160263 A129461 A239336 * A097579 A091549 A034904 Adjacent sequences: A203132 A203133 A203134 * A203136 A203137 A203138 KEYWORD nonn,easy AUTHOR Ant King, Dec 30 2011 STATUS approved

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Last modified June 16 07:19 EDT 2024. Contains 373423 sequences. (Running on oeis4.)