A192136 a(n) = (5*n^2 - 3*n + 2)/2.
1, 2, 8, 19, 35, 56, 82, 113, 149, 190, 236, 287, 343, 404, 470, 541, 617, 698, 784, 875, 971, 1072, 1178, 1289, 1405, 1526, 1652, 1783, 1919, 2060, 2206, 2357, 2513, 2674, 2840, 3011, 3187, 3368, 3554, 3745, 3941, 4142, 4348, 4559, 4775, 4996, 5222, 5453, 5689
Offset: 0
Links
- Vincenzo Librandi, 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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Magma
A192136:=func< n | (5*n^2-3*n+2)/2 >; [ A192136(n): n in [0..50] ]; // Klaus Brockhaus, Jun 27 2011
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Mathematica
Table[(5n^2-3n+2)/2,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{1,2,8},50] (* Harvey P. Dale, Aug 08 2016 *) -
PARI
a(n)=n*(5*n-3)/2+1 \\ Charles R Greathouse IV, Jun 17 2017
Formula
a(n) = (5*n^2 - 3*n + 2)/2.
a(n) = 2*a(n-1) - a(n-2) + 5.
a(n) = a(n-1) + 5*n - 4.
a(n) = 5*binomial(n+2,2) - 9*n - 4.
a(n) = A000217(n+1) - A000217(n) + 5*A000217(n-1); triangular numbers. - Johannes W. Meijer, Jul 07 2011
O.g.f.: (1-x+5*x^2)/(1-x)^3.
From Elmo R. Oliveira, Nov 16 2024: (Start)
E.g.f.: exp(x)*(2 + 2*x + 5*x^2)/2.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
Comments