A145910 a(n) = (1 + 3*n)*(4 + 3*n)/2.
2, 14, 35, 65, 104, 152, 209, 275, 350, 434, 527, 629, 740, 860, 989, 1127, 1274, 1430, 1595, 1769, 1952, 2144, 2345, 2555, 2774, 3002, 3239, 3485, 3740, 4004, 4277, 4559, 4850, 5150, 5459, 5777, 6104, 6440, 6785, 7139, 7502, 7874
Offset: 0
Links
- R. C. Alperin, A nonlinear recurrence and its relations to Chebyshev polynomials, Fib. Q., Vol. 58, No. 2 (2020), 140-142.
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Maple
A145910:=n->(1+3*n)*(4+3*n)/2: seq(A145910(n), n=0..100); # Wesley Ivan Hurt, Jul 25 2017
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Mathematica
Table[(1+3n)(4+3n)/2, {n,0,50}] (* Harvey P. Dale, Feb 23 2011 *) -
PARI
a(n)=(1+3*n)*(4+3*n)/2 \\ Charles R Greathouse IV, Jun 17 2017
Formula
a(n) = a(n-1) + 3*(3*n+1) = a(n-1) + A017197(n+1).
G.f.: (-2 - 8*x + x^2)/(x-1)^3. - R. J. Mathar, Jan 06 2011
a(n) = A144449(n)/8.
a(n) = 2*a(n-1) - a(n-2) + 9.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
From Amiram Eldar, Mar 11 2022: (Start)
Sum_{n>=0} 1/a(n) = 2/3.
Sum_{n>=0} (-1)^n/a(n) = 4*Pi/(9*sqrt(3)) + 4*log(2)/9 - 2/3. (End)
From Elmo R. Oliveira, Nov 15 2024: (Start)
E.g.f.: exp(x)*(4 + 24*x + 9*x^2)/2.
a(n) = A085001(n)/2. (End)
Extensions
Terms a(11)-a(42) from Vincenzo Librandi, Nov 17 2009