A168547 a(n) = 1 - 2*n^2 + 4*n*(1 + 2*n^2)/3.
1, 3, 17, 59, 145, 291, 513, 827, 1249, 1795, 2481, 3323, 4337, 5539, 6945, 8571, 10433, 12547, 14929, 17595, 20561, 23843, 27457, 31419, 35745, 40451, 45553, 51067, 57009, 63395, 70241, 77563, 85377, 93699, 102545, 111931, 121873, 132387, 143489, 155195
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Magma
[1-2*n^2+4*n*(1+2*n^2)/3: n in [0..50] ]; // Vincenzo Librandi, Aug 06 2011
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Mathematica
Table[1-2*n^2+4*n*(1+2*n^2)/3, {n,0,50}] (* G. C. Greubel, Jul 26 2016 *) LinearRecurrence[{4,-6,4,-1},{1,3,17,59},60] (* Harvey P. Dale, May 21 2023 *) -
PARI
a(n)=1-2*n^2+4*n*(1+2*n^2)/3 \\ Charles R Greathouse IV, Jul 26 2016
Formula
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
G.f.: (1 - x + 11*x^2 + 5*x^3)/(x-1)^4.
First differences: a(n+1) - a(n) = 2*A054569(n+1).
Second differences: a(n+2) - 2*a(n+1) + a(n) = 4*A004767(n).
Third differences: a(n+3) - 3*a(n+2) + 3*a(n+1) - a(n) = 16.
a(n) = 1 - 2*n^2 + 4*A005900(n). - R. J. Mathar, Dec 05 2009
E.g.f.: (1/3)*(3 + 6*x + 18*x^2 + 8*x^3)*exp(x). - G. C. Greubel, Jul 26 2016
Extensions
Edited and extended by R. J. Mathar, Dec 05 2009
Comments