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A154599
a(n) = 2*n^2 + 20*n + 8.
1
30, 56, 86, 120, 158, 200, 246, 296, 350, 408, 470, 536, 606, 680, 758, 840, 926, 1016, 1110, 1208, 1310, 1416, 1526, 1640, 1758, 1880, 2006, 2136, 2270, 2408, 2550, 2696, 2846, 3000, 3158, 3320, 3486, 3656, 3830, 4008, 4190, 4376, 4566, 4760, 4958, 5160
OFFSET
1,1
COMMENTS
Tenth diagonal of A144562.
2*a(n) + 84 is a square.
FORMULA
From R. J. Mathar, Jan 05 2011: (Start)
a(n) = 2*A127147(n+13).
G.f.: 2*x*(5-4*x)*(3-x)/(1-x)^3. (End)
From Amiram Eldar, Feb 25 2023: (Start)
Sum_{n>=1} 1/a(n) = 79/952 - cot(sqrt(21)*Pi)*Pi/(4*sqrt(21)).
Sum_{n>=1} (-1)^(n+1)/a(n) = 2851/14280 - cosec(sqrt(21)*Pi)*Pi/(4*sqrt(21)). (End)
E.g.f.: 2*(-4 + (4 + 11*x + x^2)*exp(x)). - G. C. Greubel, May 30 2024
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {30, 56, 86}, 50] (* Vincenzo Librandi, Feb 26 2012 *)
Table[2n^2+20n+8, {n, 50}] (* Harvey P. Dale, Jun 15 2019 *)
PROG
(Magma) I:=[30, 56, 86]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 26 2012
(PARI) for(n=1, 40, print1(2*n^2+20*n+8", ")); \\ Vincenzo Librandi, Feb 26 2012
(SageMath) [2*n^2+20*n+8 for n in range(1, 41)] # G. C. Greubel, May 30 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jan 12 2009
STATUS
approved