A153260 a(n) = n^3 - 3*(n+3)^2.
-27, -47, -67, -81, -83, -67, -27, 43, 149, 297, 493, 743, 1053, 1429, 1877, 2403, 3013, 3713, 4509, 5407, 6413, 7533, 8773, 10139, 11637, 13273, 15053, 16983, 19069, 21317, 23733, 26323, 29093, 32049, 35197, 38543, 42093, 45853, 49829, 54027
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
[n^3-3*(n+3)^2: n in [0..40] ]; // Vincenzo Librandi, Aug 25 2011
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Mathematica
a[n_]:=n^3-3*(n+3)^2; a/@ Range[0, 50] Table[n^3-3(n+3)^2,{n,0,50}] (* or *) LinearRecurrence[{4,-6,4,-1},{-27,-47,-67,-81},51] (* Harvey P. Dale, Aug 24 2011 *) -
PARI
vector(40, n, n--; n^3-3*(n+3)^2) \\ G. C. Greubel, Nov 10 2018
Formula
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(0)=-27, a(1)=-47, a(2)=-67, a(3)=-81. - Harvey P. Dale, Aug 24 2011
G.f.: (x*(x*(13*x - 41) + 61) - 27)/(x-1)^4. - Harvey P. Dale, Aug 24 2011
E.g.f.: (-27 - 20*x + x^3)*exp(x). - G. C. Greubel, Nov 10 2018
Extensions
Offset changed from 1 to 0 by Vincenzo Librandi, Aug 25 2011