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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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Also positive integers x in the solutions to 3*x^2-5*y^2-x+5*y-2 = 0, the corresponding values of y being A253470.
LINKS
FORMULA
a(n) = 9*a(n-1)-9*a(n-2)+a(n-3).
G.f.: -x*(x^2-3*x+1) / ((x-1)*(x^2-8*x+1)).
a(n) = (2-(-5+sqrt(15))*(4+sqrt(15))^n+(4-sqrt(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^2-3*x+1)/((x-1)*(x^2-8*x+1)) + O(x^100))
CROSSREFS
Sequence in context: A155598 A190005 A334609 * A301421 A288689 A271933
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jan 07 2015
STATUS
approved

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Last modified April 14 20:39 EDT 2024. Contains 371667 sequences. (Running on oeis4.)