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

0,1

References

R. C. Alperin, A nonlinear recurrence and its relations to Chebyshev polynomials, Fib. Q., Vol. 58, No. 2 (2020), pp. 140-142.

Links

Table of n, a(n) for n=0..41.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

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)

Maple

A145910:=n->(1+3*n)*(4+3*n)/2: seq(A145910(n), n=0..100); # Wesley Ivan Hurt, Jul 25 2017

Mathematica

Table[(1+3n)(4+3n)/2, {n, 0, 50}] (* Harvey P. Dale, Feb 23 2011 *)

Prog

(PARI) a(n)=(1+3*n)*(4+3*n)/2 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A017197, A085001, A144449.

Sequence in context: A324043 A230894 A291152 * A128126 A367646 A367578

Adjacent sequences: A145907 A145908 A145909 * A145911 A145912 A145913

Keyword

nonn,easy

Author

Paul Curtz, Oct 24 2008

Extensions

Terms a(11)-a(42) from Vincenzo Librandi, Nov 17 2009

Status

approved