login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A203134 Decagonal hexagonal numbers 2
1, 1540, 1777555, 2051297326, 2367195337045, 2731741367653000, 3152427171076225351, 3637898223680596402450, 4198131397700237172202345, 4844639995047850016125104076, 5590710356153821218371197901755, 6451674906361514638150346253521590 (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))^8 = 577+408*sqrt(2).
LINKS
FORMULA
G.f.: x*(1+385*x+10*x^2) / ((1-x)*(1-1154*x+x^2)).
a(n) = 1155*a(n-1)-1155*a(n-2)+a(n-3).
a(n) = 1154*a(n-1)-a(n-2)+396.
a(n) = (1/64)*((5*sqrt(2)-1)*(sqrt(2)+1)^(8*n-5)+ (5*sqrt(2)+1)*(sqrt(2)-1)^(8*n-5)-22).
a(n) = floor(1/64 *(5*sqrt(2)-1)*(sqrt(2)+1)^(8*n-5)).
EXAMPLE
The second number which is both hexagonal and decagonal is 1540. Hence a(2) = 1540.
MATHEMATICA
LinearRecurrence[{1155, -1155, 1}, {1, 1540, 1777555}, 12]
CROSSREFS
Sequence in context: A237400 A200429 A092717 * A083734 A137598 A252966
KEYWORD
nonn,easy
AUTHOR
Ant King, Dec 30 2011
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 18 21:02 EDT 2024. Contains 374388 sequences. (Running on oeis4.)