

A048903


Heptagonal hexagonal numbers.


2




OFFSET

1,2


COMMENTS

As n increases, this sequence is approximately geometric with common ratio r = lim(n>Infinity,a(n)/a(n1)) = (2+sqrt(5))^8 = 51841+23184*sqrt(5).  Ant King, Dec 24 2011


LINKS

Table of n, a(n) for n=1..8.
Eric Weisstein's World of Mathematics, Heptagonal Hexagonal Number
Index to sequences with linear recurrences with constant coefficients, signature (103683,103683,1).


FORMULA

Contribution from Ant King, Dec 24 2011: (Start)
G.f.: x*(1+18088*x+55*x^2)/((1x)*(1103682*x+x^2)).
a(n) = 103683*a(n1)103683*a(n2)+a(n3).
a(n) = 103682*a(n1)a(n2)+18144.
a(n) = 1/80*((sqrt(5)1)*(2+sqrt(5))^(8n5) (sqrt(5)+1)*(2sqrt(5))^(8n5)14).
a(n) = floor(1/80*(sqrt(5)1)*(2+sqrt(5))^(8n5)).
(End)


MATHEMATICA

LinearRecurrence[{103683, 103683, 1}, {1, 121771, 12625478965}, 8]; (* Ant King, Dec 24 2011 *)


CROSSREFS

Cf. A048901, A048902.
Sequence in context: A135495 A067384 A066881 * A237793 A185864 A236797
Adjacent sequences: A048900 A048901 A048902 * A048904 A048905 A048906


KEYWORD

nonn,easy


AUTHOR

Eric W. Weisstein


STATUS

approved



