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!)
A133272 Indices of centered heptagonal numbers (A069099) which are also heptagonal numbers (A000566). 3
1, 7, 78, 924, 11005, 131131, 1562562, 18619608, 221872729, 2643853135, 31504364886, 375408525492, 4473397941013, 53305366766659, 635191003258890, 7568986672340016, 90192649064821297, 1074742802105515543 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Numbers X such that 140*X^2-140*X+49 is a square.
Also positive integers x in the solutions to 5*x^2 - 7*y^2 - 5*x + 7*y = 0, the corresponding values of y being A253621. - Colin Barker, Jan 06 2015
Also indices of centered pentagonal numbers (A005891) which are also centered heptagonal numbers (A069099). - Colin Barker, Jan 06 2015
LINKS
FORMULA
a(n+2) = 12*a(n+1) - a(n) - 5.
a(n+1) = 6*a(n) - 5/2 + (1/2)*sqrt(140*a(n)^2 - 140*a(n) + 49).
G.f.: x*(-1+6*x)/((-1+x)*(1-12*x+x^2)). - R. J. Mathar, Nov 14 2007
a(n) = 13*a(n-1) - 13*a(n-2) + a(n-3). - Colin Barker, Jan 06 2015
MATHEMATICA
LinearRecurrence[{13, -13, 1}, {1, 7, 78}, 25] (* Paolo Xausa, Jan 07 2024 *)
PROG
(PARI) Vec(x*(6*x-1)/((x-1)*(x^2-12*x+1)) + O(x^100)) \\ Colin Barker, Jan 06 2015
CROSSREFS
Sequence in context: A045485 A068621 A210406 * A186657 A079590 A202755
KEYWORD
nonn,easy
AUTHOR
Richard Choulet, Oct 16 2007
EXTENSIONS
More terms from Paolo P. Lava, Jul 14 2008
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 March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)