The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
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!)
A254654 Pentagonal numbers (A000326) which are also centered heptagonal numbers (A069099). 3
1, 22, 11572, 265651, 139997551, 3213845272, 1693690359922, 38881099834501, 20490265834338301, 470383542583947322, 247891234370134405072, 5690700059299494866551, 2998988132919620198222251, 68846088847021746311586172, 36281758184170330787958387022 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
a(n) = a(n-1)+12098*a(n-2)-12098*a(n-3)-a(n-4)+a(n-5).
G.f.: -x*(x^4+21*x^3-548*x^2+21*x+1) / ((x-1)*(x^2-110*x+1)*(x^2+110*x+1)).
EXAMPLE
22 is in the sequence because it is the 4th pentagonal number and the 3rd centered heptagonal number.
MATHEMATICA
CoefficientList[Series[(x^4 + 21*x^3 - 548*x^2 + 21*x + 1)/((1 - x)*(x^2 - 110*x + 1)*(x^2 + 110*x + 1)), {x, 0, 20}], x] (* Wesley Ivan Hurt, Jan 19 2017 *)
PROG
(PARI) Vec(-x*(x^4+21*x^3-548*x^2+21*x+1)/((x-1)*(x^2-110*x+1)*(x^2+110*x+1)) + O(x^100))
(Magma) I:=[1, 22, 11572, 265651, 139997551]; [n le 5 select I[n] else Self(n-1)+12098*Self(n-2)-12098*Self(n-3)-Self(n-4)+Self(n-5): n in [1..20]]; // Vincenzo Librandi, Jan 20 2017
CROSSREFS
Sequence in context: A013727 A370314 A229346 * A028692 A127486 A232847
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Feb 04 2015
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 June 17 09:14 EDT 2024. Contains 373444 sequences. (Running on oeis4.)