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A161712 a(n) = (4*n^3 - 6*n^2 + 8*n + 3)/3. 17

%I

%S 1,3,9,27,65,131,233,379,577,835,1161,1563,2049,2627,3305,4091,4993,

%T 6019,7177,8475,9921,11523,13289,15227,17345,19651,22153,24859,27777,

%U 30915,34281,37883,41729,45827,50185,54811,59713,64899,70377,76155

%N a(n) = (4*n^3 - 6*n^2 + 8*n + 3)/3.

%C {a(k): 0 <= k < 4} = divisors of 27:

%C a(n) = A027750(A006218(26) + k + 1), 0 <= k < A000005(27).

%H Vincenzo Librandi, <a href="/A161712/b161712.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) + 2*C(n,1) + 4*C(n,2) + 8*C(n,3).

%F G.f.: ((x+1)(1+x(5x-2)))/(x-1)^4. - _Harvey P. Dale_, Apr 13 2011

%F E.g.f.: (1/3)*(4*x^3 + 6*x^2 + 6*x + 3)*exp(x). - _G. C. Greubel_, Jul 16 2017

%e Differences of divisors of 27 to compute the coefficients of their interpolating polynomial, see formula:

%e 1 3 9 27

%e 2 6 18

%e 4 12

%e 8

%t Table[(4n^3-6n^2+8n+3)/3,{n,0,80}] (* _Harvey P. Dale_, Apr 13 2011 *)

%o (PARI) a(n)=(4*n^3-6*n^2+8*n)/3+1 \\ _Charles R Greathouse IV_, Jul 16, 2011

%o (MAGMA) [(4*n^3 - 6*n^2 + 8*n + 3)/3: n in [0..40]]; // _Vincenzo Librandi_, Jul 17 2011

%K nonn,easy

%O 0,2

%A _Reinhard Zumkeller_, Jun 17 2009

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Last modified August 10 08:28 EDT 2020. Contains 336368 sequences. (Running on oeis4.)