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 A203408 Numbers which are both heptagonal and decagonal. 2
 1, 540, 2887450, 1123674201, 6004054625647, 2336525434757970, 12484603034492528512, 4858482201068079159687, 25960009135002449017962445, 10102543266574986692211140472, 53980256514964477791853933850326, 21006844571867038996088473395797925 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS As n increases, the ratios of consecutive terms settle into an approximate 2-cycle with a(n)/a(n-1) bounded above and below by 1/81*(216401+68432*sqrt(10)) and 1/81*(15761+4984*sqrt(10)) respectively. LINKS Index entries for linear recurrences with constant coefficients, signature (1,2079362,-2079362,-1,1). FORMULA G.f.: x(1+539*x+807548*x^2+10633*x^3+27*x^4) / ((1-x)*(1-1442*x+x^2)*(1+1442*x+x^2)). a(n) = 2079362*a(n-2)-a(n-4)+818748. a(n) = a(n-1)+2079362*a(n-2)-2079362*a(n-3)-a(n-4)+a(n-5). a(n) = 1/320*((11-2*sqrt(10)*(-1)^n)*(1+sqrt(10))* (3+sqrt(10))^(4*n-3)+(11+2*sqrt(10)*(-1)^n)*(1-sqrt(10))*(3-sqrt(10))^(4*n-3)-126). a(n) = floor(1/320*(11-2*sqrt(10)*(-1)^n)*(1+sqrt(10))* (3+sqrt(10))^(4*n-3)). EXAMPLE The second number that is both heptagonal and decagonal is 540. Hence a(2)=540. MATHEMATICA LinearRecurrence[{1, 2079362, -2079362, -1, 1}, {1, 540, 2887450, 1123674201, 6004054625647}, 15] CROSSREFS Cf. A203409, A203410, A001107, A000566. Sequence in context: A056934 A238933 A003746 * A259165 A293393 A146356 Adjacent sequences:  A203405 A203406 A203407 * A203409 A203410 A203411 KEYWORD nonn,easy AUTHOR Ant King, Jan 02 2012 STATUS approved

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Last modified December 1 22:24 EST 2020. Contains 338858 sequences. (Running on oeis4.)