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A322597 a(n) = (4*n^3 - 6*n^2 + 20*n + 3)/3. 0

%I

%S 1,7,17,39,81,151,257,407,609,871,1201,1607,2097,2679,3361,4151,5057,

%T 6087,7249,8551,10001,11607,13377,15319,17441,19751,22257,24967,27889,

%U 31031,34401,38007,41857,45959,50321,54951,59857,65047,70529,76311,82401,88807

%N a(n) = (4*n^3 - 6*n^2 + 20*n + 3)/3.

%C For n >= 2, a(n) gives the number of function evaluations for Dooren and Ridder's degree 5 and 7 cubature rule over an n-dimensional cube, with the exception of a(3) = 45 and a(4) = 97.

%H Ronald Cools, <a href="http://nines.cs.kuleuven.be/ecf/">Encyclopaedia of Cubature Formulas</a>

%H Paul van Dooren and Luc de Ridder, <a href="https://doi.org/10.1016/0771-050X(76)90005-X">An adaptive algorithm for numerical integration over an n-dimensional cube</a>, Journal of Computational and Applied Mathematics, Vol. 2 (1976), 207-217.

%H Alan C. Genz and Awais A. Malik, <a href="https://doi.org/10.1016/0771-050X(80)90039-X">Remarks on algorithm 006: An adaptive algorithm for numerical integration over an N-dimensional rectangular region</a>, Journal of Computational and Applied Mathematics, Vol. 6 (1980), 295-302.

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

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), n >= 4.

%F G.f.: (1 + 3*x - 5*x^2 + 9*x^3)/((1 - x)^4).

%F E.g.f.: (1/3)*(3 + 18*x + 6*x^2 + 4*x^3)*exp(x).

%p [(4*n^3-6*n^2+20*n+3)/3$n=0..50]; # _Muniru A Asiru_, Jan 23 2019

%t Table[(4*n^3 - 6*n^2 + 20*n + 3)/3, {n, 0, 50}]

%o (Maxima) makelist((4*n^3 - 6*n^2 + 20*n + 3)/3, n, 0, 50);

%Y First differences: 2*A093328.

%Y Cf. A174794, A321124, A322594, A322595.

%K nonn,easy

%O 0,2

%A _Franck Maminirina Ramaharo_, Jan 23 2019

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Last modified July 30 07:41 EDT 2021. Contains 346348 sequences. (Running on oeis4.)