

A203408


Numbers which are both heptagonal and decagonal.


2



1, 540, 2887450, 1123674201, 6004054625647, 2336525434757970, 12484603034492528512, 4858482201068079159687, 25960009135002449017962445, 10102543266574986692211140472, 53980256514964477791853933850326, 21006844571867038996088473395797925
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OFFSET

1,2


COMMENTS

As n increases, the ratios of consecutive terms settle into an approximate 2cycle with a(n)/a(n1) bounded above and below by 1/81*(216401+68432*sqrt(10)) and 1/81*(15761+4984*sqrt(10)) respectively.


LINKS

Table of n, a(n) for n=1..12.
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) / ((1x)*(11442*x+x^2)*(1+1442*x+x^2)).
a(n) = 2079362*a(n2)a(n4)+818748.
a(n) = a(n1)+2079362*a(n2)2079362*a(n3)a(n4)+a(n5).
a(n) = 1/320*((112*sqrt(10)*(1)^n)*(1+sqrt(10))* (3+sqrt(10))^(4*n3)+(11+2*sqrt(10)*(1)^n)*(1sqrt(10))*(3sqrt(10))^(4*n3)126).
a(n) = floor(1/320*(112*sqrt(10)*(1)^n)*(1+sqrt(10))* (3+sqrt(10))^(4*n3)).


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



