login
a(n) = (-4*n^3 + 27*n^2 - 20*n + 3)/3.
18

%I #25 Sep 08 2022 08:45:45

%S 1,2,13,26,33,26,-3,-62,-159,-302,-499,-758,-1087,-1494,-1987,-2574,

%T -3263,-4062,-4979,-6022,-7199,-8518,-9987,-11614,-13407,-15374,

%U -17523,-19862,-22399,-25142,-28099,-31278,-34687,-38334,-42227,-46374,-50783

%N a(n) = (-4*n^3 + 27*n^2 - 20*n + 3)/3.

%C {a(k): 0 <= k < 4} = divisors of 26:

%C a(n) = A027750(A006218(25) + k + 1), 0 <= k < A000005(26).

%H Vincenzo Librandi, <a href="/A161711/b161711.txt">Table of n, a(n) for n = 0..10000</a>

%H R. Zumkeller, <a href="/A161700/a161700.txt">Enumerations of Divisors</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F a(n) = C(n,0) + C(n,1) + 10*C(n,2) - 8*C(n,3).

%F G.f.: (1-2*x+11*x^2-18*x^3)/(1-x)^4. - _Bruno Berselli_, Jul 17 2011

%e Differences of divisors of 26 to compute the coefficients of their interpolating polynomial, see formula:

%e 1 2 13 26

%e 1 11 13

%e 10 2

%e -8

%t LinearRecurrence[{4,-6,4,-1},{1,2,13,26},40] (* _Harvey P. Dale_, Jul 02 2017 *)

%o (Magma) [(-4*n^3 + 27*n^2 - 20*n + 3)/3: n in [0..40]]; // _Vincenzo Librandi_, Jul 17 2011

%o (PARI) x='x+O('x^50); Vec((1-2*x+11*x^2-18*x^3)/(1-x)^4) \\ _G. C. Greubel_, Jul 16 2017

%Y Cf. A005408, A000124, A016813, A086514, A000125, A058331, A002522, A161701, A161702, A161703, A000127, A161704, A161706, A161707, A161708, A161710, A080856, A161712, A161713, A161715, A006261.

%K sign,easy

%O 0,2

%A _Reinhard Zumkeller_, Jun 17 2009