login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A253922 Indices of centered pentagonal numbers (A005891) which are also octagonal numbers (A000567). 3
1, 56, 297, 26752, 142913, 12894168, 68883529, 6214961984, 33201717825, 2995598781880, 16003159107881, 1443872397903936, 7713489488280577, 695943500190915032, 3717885930192129993, 335443323219623141248, 1792013304863118375809, 161682985848358163166264 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also positive integers y in the solutions to 6*x^2 - 5*y^2 - 4*x + 5*y - 2 = 0, the corresponding values of x being A253921.

LINKS

Colin Barker, Table of n, a(n) for n = 1..745

Index entries for linear recurrences with constant coefficients, signature (1,482,-482,-1,1).

FORMULA

a(n) = a(n-1)+482*a(n-2)-482*a(n-3)-a(n-4)+a(n-5).

G.f.: x*(55*x^3+241*x^2-55*x-1) / ((x-1)*(x^2-22*x+1)*(x^2+22*x+1)).

EXAMPLE

56 is in the sequence because the 56th centered pentagonal is 7701, which is also the number 51st octagonal number.

MATHEMATICA

CoefficientList[Series[(55 x^3 + 241 x^2 - 55 x - 1)/((x - 1)(x^2 - 22 x + 1) (x^2 + 22 x + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 20 2015 *)

PROG

(PARI) Vec(x*(55*x^3+241*x^2-55*x-1)/((x-1)*(x^2-22*x+1)*(x^2+22*x+1)) + O(x^100))

(MAGMA) I:=[1, 56, 297, 26752, 142913]; [n le 5 select I[n] else Self(n-1)+482*Self(n-2)-482*Self(n-3)-Self(n-4)+Self(n-5): n in [1..25]]; // Vincenzo Librandi, Jan 20 2015

CROSSREFS

Cf. A000567, A005891, A253921, A253923.

Sequence in context: A205235 A205228 A110554 * A220015 A005912 A264581

Adjacent sequences:  A253919 A253920 A253921 * A253923 A253924 A253925

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Jan 19 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 27 19:26 EDT 2020. Contains 338035 sequences. (Running on oeis4.)