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%I #11 Apr 14 2020 19:06:13
%S 0,2,115,1783,11758,49304,156633,412589,949564,1973662,3788095,
%T 6819827,11649450,19044308,29994853,45754249,67881208,98286074,
%U 139280139,193628207,264604390,356051152,472441585,618944933,801495348,1026863894,1302733783,1637778859,2041745314,2525536652
%N a(n) = (36*n^6 - 60*n^5 + 30*n^4 + 4*n^3 + 8*n^2 - 4*n + 1 - (-1)^n)/8.
%H Colin Barker, <a href="/A260334/b260334.txt">Table of n, a(n) for n = 0..1000</a>
%H B. T. Bennett and R. B. Potts, <a href="/A002047/a002047_1.pdf">Arrays and brooks</a>, J. Austral. Math. Soc., 7 (1967), 23-31. [Annotated scanned copy] See b_{n,3}.
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (6,-14,14,0,-14,14,-6,1).
%F G.f.: -x*(17*x^6+487*x^5+2108*x^4+2642*x^3+1121*x^2+103*x+2) / ((x-1)^7*(x+1)). - _Colin Barker_, Jul 29 2015
%t Table[(36n^6-60n^5+30n^4+4n^3+8n^2-4n+1-(-1)^n)/8,{n,0,30}] (* or *) LinearRecurrence[{6,-14,14,0,-14,14,-6,1},{0,2,115,1783,11758,49304,156633,412589},30] (* _Harvey P. Dale_, Apr 14 2020 *)
%o (PARI) concat(0, Vec(-x*(17*x^6 +487*x^5 +2108*x^4 +2642*x^3 +1121*x^2 +103*x +2) / ((x -1)^7*(x +1)) + O(x^100))) \\ _Colin Barker_, Jul 29 2015
%Y Conjectured to be the 4th diagonal of A260333.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Jul 27 2015
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