A152734 5 times pentagonal numbers: 5*n*(3*n-1)/2.
0, 5, 25, 60, 110, 175, 255, 350, 460, 585, 725, 880, 1050, 1235, 1435, 1650, 1880, 2125, 2385, 2660, 2950, 3255, 3575, 3910, 4260, 4625, 5005, 5400, 5810, 6235, 6675, 7130, 7600, 8085, 8585, 9100, 9630, 10175, 10735, 11310, 11900, 12505, 13125, 13760, 14410
Offset: 0
Examples
From _Omar E. Pol_, Aug 22 2011 (Start): Illustration of initial terms as concentric pentagons (in a precise representation the pentagons should be strictly concentric): . . o . o o . o o . o o o o . o o o o o o . o o o o o o . o o o o o o o o o .o o o o o o o o o o o o . o o o o o o o o o o o o . o o o o o o . o o o o o o . o o o o o o o o o o o o . o o . o o . o o o o o o o o . . 5 25 60 (End)
Links
- Ivan Panchenko, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Crossrefs
Programs
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Magma
[5*n*(3*n-1)/2 : n in [0..50]]; // Wesley Ivan Hurt, Sep 19 2014
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Maple
A152734:=n->5*n*(3*n-1)/2: seq(A152734(n), n=0..50); # Wesley Ivan Hurt, Sep 19 2014
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Mathematica
Table[5 n (3 n - 1)/2, {n, 0, 50}] (* Wesley Ivan Hurt, Sep 19 2014 *) 5*PolygonalNumber[5,Range[0,50]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 13 2020 *) -
PARI
a(n)=5*n*(3*n-1)/2 \\ Charles R Greathouse IV, Sep 24 2015
Formula
a(n) = 5*A000326(n).
a(n) = a(n-1)+15*n-10 (with a(0)=0). - Vincenzo Librandi, Nov 26 2010
E.g.f.: (5/2)*(3*x^2 + 2*x)*exp(x). - G. C. Greubel, Jul 17 2017
From Amiram Eldar, Feb 26 2022: (Start)
Sum_{n>=1} 1/a(n) = (9*log(3) - sqrt(3)*Pi)/15.
Sum_{n>=1} (-1)^(n+1)/a(n) = 2*(sqrt(3)*Pi- 6*log(2))/15. (End)
Comments