A082112 a(n) = 4*n^2 + 10*n + 1.
1, 15, 37, 67, 105, 151, 205, 267, 337, 415, 501, 595, 697, 807, 925, 1051, 1185, 1327, 1477, 1635, 1801, 1975, 2157, 2347, 2545, 2751, 2965, 3187, 3417, 3655, 3901, 4155, 4417, 4687, 4965, 5251, 5545, 5847, 6157, 6475, 6801, 7135, 7477, 7827, 8185, 8551
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Magma
[4*n^2 + 10*n + 1 : n in [0..50]]; // Wesley Ivan Hurt, Dec 22 2021
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Mathematica
Table[n +(n+1)^2 -4, {n,1,200, 2}] (* Vladimir Joseph Stephan Orlovsky, Jun 26 2011 *) LinearRecurrence[{3,-3,1},{1,15,37},50] (* Harvey P. Dale, Dec 18 2014 *) -
PARI
a(n)=4*n^2+10*n+1 \\ Charles R Greathouse IV, Jun 17 2017
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SageMath
[4*n^2+10*n+1 for n in range(51)] # G. C. Greubel, Dec 22 2022
Formula
a(n) = a(n-1) + 8*n + 6 (with a(0)=1). - Vincenzo Librandi, Aug 08 2010
G.f.: (1+12*x-5*x^2) / (1-x)^3. - R. J. Mathar, Dec 03 2014
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Wesley Ivan Hurt, Dec 22 2021
E.g.f.: (1 + 14*x + 4*x^2)*exp(x). - G. C. Greubel, Dec 22 2022
Comments