|
%I M5292 #26 Oct 20 2022 21:47:39
%S 1,48,186,416,738,1152,1658,2256,2946,3728,4602,5568,6626,7776,9018,
%T 10352,11778,13296,14906,16608,18402,20288,22266,24336,26498,28752,
%U 31098,33536,36066,38688,41402,44208,47106,50096,53178,56352,59618,62976,66426,69968
%N Number of points on surface of truncated cube: 46n^2 + 2.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1).
%F a(0)=1, a(1)=48, a(2)=186, a(3)=416, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - _Harvey P. Dale_, Aug 19 2014
%p A005911:=-(z+1)*(z**2+44*z+1)/(z-1)**3; [Conjectured by _Simon Plouffe_ in his 1992 dissertation.]
%t Join[{1},Table[46n^2+2,{n,50}]] (* or *) Join[{1},LinearRecurrence[{3,-3,1},{48,186,416},50]] (* _Harvey P. Dale_, Aug 19 2014 *)
%o (PARI) a(n)=if(n, 46*n^2+2, 1) \\ _Charles R Greathouse IV_, Oct 20 2022
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
%E More terms from _Harvey P. Dale_, Aug 19 2014
|
