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A178977
a(n) = (3*n+2)*(3*n+5)/2.
3
5, 20, 44, 77, 119, 170, 230, 299, 377, 464, 560, 665, 779, 902, 1034, 1175, 1325, 1484, 1652, 1829, 2015, 2210, 2414, 2627, 2849, 3080, 3320, 3569, 3827, 4094, 4370, 4655, 4949, 5252, 5564, 5885, 6215, 6554, 6902, 7259, 7625, 8000, 8384, 8777, 9179, 9590, 10010
OFFSET
0,1
COMMENTS
Companion to A145910.
FORMULA
a(n) = a(n-1) + 6 + 9*n.
a(n) = A178971(3*n+2).
a(n) = A145910(n) + 3 + 3*n = A145910(n) + A008585(n+1).
a(n) = A168233(n+1)*A168300(n+1).
G.f.: (-5-5*x+x^2)/(x-1)^3. [Adapted to the offset by Bruno Berselli, Apr 14 2011]
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Apr 19 2013
From Amiram Eldar, Mar 10 2022: (Start)
Sum_{n>=0} 1/a(n) = 1/3.
Sum_{n>=0} (-1)^n/a(n) = 4*Pi/(9*sqrt(3)) - 1/3 - 4*log(2)/9. (End)
From Elmo R. Oliveira, Oct 30 2024: (Start)
E.g.f.: exp(x)*exp(x)*(5 + 15*x + 9*x^2/2).
a(n) = A016789(n)*A016789(n+1)/2. (End)
MAPLE
A178977:=n->(3*n+2)*(3*n+5)/2: seq(A178977(n), n=0..50); # Wesley Ivan Hurt, Oct 23 2014
MATHEMATICA
f[n_] := (3 n + 2) (3 n + 5)/2; Array[f, 45, 0]
LinearRecurrence[{3, -3, 1}, {5, 20, 44}, 50] (* Harvey P. Dale, Apr 19 2013 *)
PROG
(Magma) [n*(n+3)/2: n in [2..135 by 3]]; // Bruno Berselli, Apr 14 2011
(PARI) a(n)=(3*n+2)*(3*n+5)/2 \\ Charles R Greathouse IV, Jun 17 2017
KEYWORD
nonn,easy,changed
AUTHOR
Paul Curtz, Jan 02 2011
STATUS
approved