A144312 a(n) = 5*n*(5*n + 1)/2.
0, 15, 55, 120, 210, 325, 465, 630, 820, 1035, 1275, 1540, 1830, 2145, 2485, 2850, 3240, 3655, 4095, 4560, 5050, 5565, 6105, 6670, 7260, 7875, 8515, 9180, 9870, 10585, 11325, 12090, 12880, 13695, 14535, 15400, 16290, 17205, 18145, 19110, 20100
Offset: 0
Links
- Stefano Spezia, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Mathematica
a[n_] := 5*n*(5*n+1)/2; Array[a, 50, 0] (* Amiram Eldar, May 10 2025 *)
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PARI
a(n)=5*n*(5*n+1)/2 \\ Charles R Greathouse IV, Jun 17 2017
Formula
a(n) = A000217(5*n).
a(n) = a(n-1) + 25*n - 10 (with a(0) = 0). - Vincenzo Librandi, Nov 25 2010
From Stefano Spezia, Jun 12 2021: (Start)
O.g.f.: 5*x*(3 + 2*x)/(1 - x)^3.
E.g.f.: 5*exp(x)*x*(6 + 5*x)/2.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
From Amiram Eldar, May 10 2025: (Start)
Sum_{n>=1} 1/a(n) = 2 - log(5)/2 - sqrt(1+2/sqrt(5))*Pi/5 - log(phi)/sqrt(5), where phi is the golden ratio (A001622).
Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/5 + sqrt(2+2/sqrt(5))*Pi/5 + 2*log(phi)/sqrt(5) - 2. (End)