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A322593 a(n) = 2^n + 2*n^2 + 1.

%I A322593 #20 Dec 15 2024 07:58:25
%S A322593 2,5,13,27,49,83,137,227,385,675,1225,2291,4385,8531,16777,33219,
%T A322593 66049,131651,262793,525011,1049377,2098035,4195273,8389667,16778369,
%U A322593 33555683,67110217,134219187,268437025,536872595,1073743625,2147485571,4294969345,8589936771
%N A322593 a(n) = 2^n + 2*n^2 + 1.
%C A322593 For n = 3..7, a(n) is the number of evaluating points on the n-dimensional sphere (also n-space with weight function exp(-r^2) or exp(-r)) in a degree 7 cubature rule.
%D A322593 Arthur H. Stroud, Approximate calculation of multiple integrals, Prentice-Hall, 1971.
%H A322593 Marius A. Burtea, <a href="/A322593/b322593.txt">Table of n, a(n) for n = 0..200</a>
%H A322593 Ronald Cools, <a href="http://nines.cs.kuleuven.be/ecf/">Encyclopaedia of Cubature Formulas</a>
%H A322593 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,7,-2).
%F A322593 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), n >= 4.
%F A322593 a(n) = a(n-1) + A100315(n-1), n >= 2.
%F A322593 G.f.: (2 - 5*x + 6*x^2 - 7*x^3)/((1 - 2*x)*(1 - x)^3)
%F A322593 E.g.f.: exp(2*x) + (1 + 2*x + 2*x^2)*exp(x).
%t A322593 Table[2^n + 2*n^2 + 1, {n, 0, 50}]
%t A322593 LinearRecurrence[{5,-9,7,-2},{2,5,13,27},50] (* _Harvey P. Dale_, Mar 23 2021 *)
%o A322593 (Maxima) makelist(2^n + 2*n^2 + 1, n, 0, 50);
%o A322593 (Magma) [2^n + 2*n^2 + 1: n in [0..33]]; // _Marius A. Burtea_, Dec 28 2018
%Y A322593 Cf. A000051, A000079, A001580, A001787, A002064, A005126, A058331, A100314, A131830, A100314, A132750, A176691, A321123.
%K A322593 nonn,easy
%O A322593 0,1
%A A322593 _Franck Maminirina Ramaharo_, Dec 18 2018