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A172193
a(n) = 5*n^2 + 31*n + 1.
1
1, 37, 83, 139, 205, 281, 367, 463, 569, 685, 811, 947, 1093, 1249, 1415, 1591, 1777, 1973, 2179, 2395, 2621, 2857, 3103, 3359, 3625, 3901, 4187, 4483, 4789, 5105, 5431, 5767, 6113, 6469, 6835, 7211, 7597, 7993, 8399, 8815, 9241, 9677, 10123, 10579
OFFSET
0,2
FORMULA
G.f.: (1+34*x-25*x^2)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Apr 07 2013
E.g.f.: (1 + 36*x + 5*x^2)*exp(x). - G. C. Greubel, Apr 28 2022
MATHEMATICA
CoefficientList[Series[(1 +34x -25x^2)/(1-x)^3, {x, 0, 60}], x] (* Vincenzo Librandi, Apr 07 2013 *)
PROG
(Magma) [ 5*n^2+31*n+1: n in [0..50] ];
(PARI) a(n)=5*n^2+31*n+1 \\ Charles R Greathouse IV, Jun 17 2017
(SageMath) [((10*n+31)^2 -941)/20 for n in (0..50)] # G. C. Greubel, Apr 28 2022
CROSSREFS
Cf. A172043 (5*n^2-n+1).
Sequence in context: A262566 A323428 A299217 * A141918 A063325 A044175
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jan 29 2010
EXTENSIONS
Replaced definition with formula. - N. J. A. Sloane, Mar 03 2010
STATUS
approved