A154590 a(n) = 2*n^2 + 16*n + 6.
24, 46, 72, 102, 136, 174, 216, 262, 312, 366, 424, 486, 552, 622, 696, 774, 856, 942, 1032, 1126, 1224, 1326, 1432, 1542, 1656, 1774, 1896, 2022, 2152, 2286, 2424, 2566, 2712, 2862, 3016, 3174, 3336, 3502, 3672, 3846, 4024, 4206, 4392, 4582, 4776, 4974, 5176
Offset: 1
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Mathematica
Table[2n^2+16n+6,{n,50}] (* or *) LinearRecurrence[{3,-3,1},{24,46,72},50] (* Harvey P. Dale, Dec 27 2011 *) -
PARI
a(n)=2*n^2+16*n+6 \\ Charles R Greathouse IV, Jun 17 2017
Formula
a(n) = 2*A116711(n+3).
G.f.: -2*x*(3*x-4)*(x-3)/(x-1)^3.
From Amiram Eldar, Mar 02 2023: (Start)
Sum_{n>=1} 1/a(n) = 35/468 - cot(sqrt(13)*Pi)*Pi/(4*sqrt(13)).
Sum_{n>=1} (-1)^(n+1)/a(n) = 121/468 + cosec(sqrt(13)*Pi)*Pi/(4*sqrt(13)). (End)
From Elmo R. Oliveira, Jun 04 2025: (Start)
E.g.f.: 2*(exp(x)*(x^2 + 9*x + 3) - 3).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
Extensions
Corrected (a(31) added) by Harvey P. Dale, Dec 27 2011
Comments