

A253411


Indices of centered octagonal numbers (A016754) which are also centered pentagonal numbers (A005891).


3



1, 76, 646, 108871, 930811, 156991186, 1342228096, 226381180621, 1935491982901, 326441505463576, 2790978097114426, 470728424497295251, 4024588480547018671, 678790061683594287646, 5803453797970703808436, 978814798219318465489561, 8368576352085274344745321
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Also positive integers y in the solutions to 5*x^2  8*y^2  5*x + 8*y = 0, the corresponding values of x being A253410.


LINKS

Colin Barker, Table of n, a(n) for n = 1..633
Index entries for linear recurrences with constant coefficients, signature (1,1442,1442,1,1).


FORMULA

a(n) = a(n1) + 1442*a(n2)  1442*a(n3)  a(n4) + a(n5).
G.f.: x*(x^4 + 75*x^3  872*x^2 + 75*x + 1) / ((x1)*(x^2  38*x + 1)*(x^2 + 38*x + 1)).


EXAMPLE

76 is in the sequence because the 76th centered octagonal number is 22801, which is also the 96th centered pentagonal number.


MATHEMATICA

LinearRecurrence[{1, 1442, 1442, 1, 1}, {1, 76, 646, 108871, 930811}, 20] (* Harvey P. Dale, Feb 04 2016 *)


PROG

(PARI) Vec(x*(x^4+75*x^3872*x^2+75*x+1)/((x1)*(x^238*x+1)*(x^2+38*x+1)) + O(x^100))


CROSSREFS

Cf. A005891, A016754, A253410, A253579.
Sequence in context: A129626 A200167 A178262 * A185481 A007250 A137061
Adjacent sequences: A253408 A253409 A253410 * A253412 A253413 A253414


KEYWORD

nonn,easy


AUTHOR

Colin Barker, Dec 31 2014


STATUS

approved



