

A048900


Heptagonal pentagonal numbers.


2



1, 4347, 16701685, 64167869935, 246532939589097, 947179489733441251, 3639063353022941697757, 13981280455134652269341655, 53716075869563980995868941265, 206377149509584359851476202998987
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OFFSET

1,2


COMMENTS

As n increases, this sequence is approximately geometric with common ratio r=lim(n>Infinity,a(n)/a(n1))=(4+sqrt(15))^4=1921+496*sqrt(15).  Ant King, Dec 15 2011


LINKS

Table of n, a(n) for n=1..10.
Eric Weisstein's World of Mathematics, Heptagonal Pentagonal Number.


FORMULA

From Ant King, Dec 15 2011: (Start)
a(n) = 3843*a(n1)  3843*a(n2) + a(n3).
a(n) = 3842*a(n1)  a(n2) + 512.
a(n) = 1/240*((2+sqrt(15))^2*(4+sqrt(15))^(4n3)+ (2sqrt(15))^2*(4sqrt(15))^(4n3)32).
a(n) = floor(1/240*((2+sqrt(15))^2*(4+sqrt(15))^(4n3))).
GF: x*(1+504*x+7*x^2)/((1x)*(13842*x+x^2)).
(End)


MATHEMATICA

LinearRecurrence[{3843, 3843, 1}, {1, 4347, 16701685}, 10] (* Ant King, Dec 15 2011 *)


CROSSREFS

Cf. A046198, A046199.
Sequence in context: A252431 A251947 A145916 * A252302 A235066 A170786
Adjacent sequences: A048897 A048898 A048899 * A048901 A048902 A048903


KEYWORD

nonn,easy


AUTHOR

Eric W. Weisstein


STATUS

approved



