

A253654


Indices of pentagonal numbers (A000326) which are also centered pentagonal numbers (A005891).


3



1, 6, 46, 361, 2841, 22366, 176086, 1386321, 10914481, 85929526, 676521726, 5326244281, 41933432521, 330141215886, 2599196294566, 20463429140641, 161108236830561, 1268402465503846, 9986111487200206, 78620489432097801, 618977803969582201, 4873201942324559806
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OFFSET

1,2


COMMENTS

Also positive integers x in the solutions to 3*x^25*y^2x+5*y2 = 0, the corresponding values of y being A253470.


LINKS

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (9,9,1).


FORMULA

a(n) = 9*a(n1)9*a(n2)+a(n3).
G.f.: x*(x^23*x+1) / ((x1)*(x^28*x+1)).
a(n) = (2(5+sqrt(15))*(4+sqrt(15))^n+(4sqrt(15))^n*(5+sqrt(15)))/12.  Colin Barker, Mar 03 2016


EXAMPLE

6 is in the sequence because the 6th pentagonal number is 51, which is also the 5th centered pentagonal number.


MATHEMATICA

LinearRecurrence[{9, 9, 1}, {1, 6, 46}, 30] (* Harvey P. Dale, Nov 12 2017 *)


PROG

(PARI) Vec(x*(x^23*x+1)/((x1)*(x^28*x+1)) + O(x^100))


CROSSREFS

Cf. A000326, A005891, A128917, A253470.
Sequence in context: A155598 A190005 A334609 * A301421 A288689 A271933
Adjacent sequences: A253651 A253652 A253653 * A253655 A253656 A253657


KEYWORD

nonn,easy


AUTHOR

Colin Barker, Jan 07 2015


STATUS

approved



