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a(n) = (n-3)*(n-8)/2.
3

%I #43 Jul 31 2022 07:49:58

%S -2,-3,-3,-2,0,3,7,12,18,25,33,42,52,63,75,88,102,117,133,150,168,187,

%T 207,228,250,273,297,322,348,375,403,432,462,493,525,558,592,627,663,

%U 700,738,777,817,858,900,943,987,1032,1078,1125,1173

%N a(n) = (n-3)*(n-8)/2.

%C Essentially a duplicate of A055998.

%H G. C. Greubel, <a href="/A167544/b167544.txt">Table of n, a(n) for n = 4..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

%F G.f.: x^4*(-2 + 3*x)/(1-x)^3.

%F a(n) = A055998(n-8). - _Philippe Deléham_, Nov 25 2009

%F a(n) = a(n-1) + n - 6 (with a(4)=-2). - _Vincenzo Librandi_, Dec 05 2010

%F a(n) = A027379(n-8) for n >= 9. - _Georg Fischer_, Oct 24 2018

%F E.g.f.: (1/2)*( (24 -10*x + x^2)*exp(x) - (24 + 14*x + 3*x^2) ). - _G. C. Greubel_, Jul 30 2022

%t Table[(n-3)*(n-8)/2, {n,4,60}] (* _G. C. Greubel_, Jun 15 2016 *)

%o (PARI) a(n)=(n-3)*(n-8)/2 \\ _Charles R Greathouse IV_, Jun 17 2017

%o (Magma) [(n-3)*(n-8)/2: n in [4..60]]; // _G. C. Greubel_, Jul 30 2022

%o (SageMath) [(n-3)*(n-8)/2 for n in (4..60)] # _G. C. Greubel_, Jul 30 2022

%Y Cf. A027379, A055998, A135929, A137276.

%K sign,easy,less

%O 4,1

%A _Jamel Ghanouchi_, Nov 06 2009

%E Edited and extended by _R. J. Mathar_, Nov 12 2009