A253654 Indices of pentagonal numbers (A000326) which are also centered pentagonal numbers (A005891).
1, 6, 46, 361, 2841, 22366, 176086, 1386321, 10914481, 85929526, 676521726, 5326244281, 41933432521, 330141215886, 2599196294566, 20463429140641, 161108236830561, 1268402465503846, 9986111487200206, 78620489432097801, 618977803969582201, 4873201942324559806
Offset: 1
Examples
6 is in the sequence because the 6th pentagonal number is 51, which is also the 5th centered pentagonal number.
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (9,-9,1).
Programs
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Mathematica
LinearRecurrence[{9,-9,1},{1,6,46},30] (* Harvey P. Dale, Nov 12 2017 *) -
PARI
Vec(-x*(x^2-3*x+1)/((x-1)*(x^2-8*x+1)) + O(x^100))
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
Comments