|
%I #16 Jan 11 2017 18:18:38
%S 1,108,3396,49852,447777,2862384,14265040,58788720,208577633,
%T 655618172,1864806372,4877412332,11877770177,27199536768,59037366080,
%U 122252641280,242826555969,464730264172,860261412132,1545252073596,2700999547873,4605325025136,7675844020560,12529356938800
%N Number of 4 X 4 traceless matrices of nonnegative integers with all row and column sums <= n.
%H Colin Barker, <a href="/A244877/b244877.txt">Table of n, a(n) for n = 0..1000</a>
%H R. P. Stanley, <a href="/A002721/a002721.pdf">Examples of Magic Labelings</a>, Unpublished Notes, 1973 [Cached copy, with permission]
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
%F G.f.: (1 + 95*x + 2070*x^2 + 13842*x^3 + 34416*x^4 + x^9 + 95*x^8 + 2070*x^7 + 13842*x^6 + 34416*x^5) / (1-x)^13.
%F a(n) = ((2+n)^2*(226800 + 1014480*n + 2137860*n^2 + 2775656*n^3 + 2422453*n^4 + 1468908*n^5 + 621705*n^6 + 180336*n^7 + 34191*n^8 + 3820*n^9 + 191*n^10)) / 907200. - _Colin Barker_, Jan 11 2017
%o (PARI) Vec((1 + 95*x + 2070*x^2 + 13842*x^3 + 34416*x^4 + x^9 + 95*x^8 + 2070*x^7 + 13842*x^6 + 34416*x^5) / (1-x)^13 + O(x^30)) \\ _Colin Barker_, Jan 11 2017
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Jul 08 2014
|
