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%I #34 Jan 04 2024 06:32:56
%S 133,1903,10561,38015,106461,252737,533397,1030505,1858149,3169675,
%T 5165641,8102491,12301949,18161133,26163389,36889845,51031685,
%U 69403143,92955217,122790103,160176349,206564729,263604837,333162401,417337317,518482403,639222873
%N a(n) = n^6 - (883/60)*n^5 + (157/3)*n^4 + (2155/12)*n^3 - (4570/3)*n^2 + (42767/15)*n - 967.
%C Old name was: "Number of stacks of n pikelets, distance 6 flips from a well-ordered stack".
%H G. C. Greubel, <a href="/A028295/b028295.txt">Table of n, a(n) for n = 6..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F G.f.: x^6*(133 + 972*x + 33*x^2 - 604*x^3 + 187*x^4 + 2*x^5 - 3*x^6) / (1-x)^7. - _R. J. Mathar_, Jun 21 2011
%F E.g.f.: (1/5!)*(116040 - 69480*x - 30540*x^2 - 2340*x^3 + 95*x^4 + 3*x^5 - (116040 - 185520*x + 96960*x^2 - 25880*x^3 + 3580*x^4 - 34*x^5 - 120*x^6)*exp(x)). - _G. C. Greubel_, Jan 03 2024
%t (* Codes from _Robert G. Wilson v_, Jul 29 2018: Start *)
%t a[n_]:= n^6 - (883/60)*n^5 + (157/3)*n^4 + (2155/12)*n^3 - (4570/3)*n^2 + (42767/15)*n - 967; Table[a[n], {n,6,36}]
%t CoefficientList[ Series[x^6 (3x^6 -2x^5 -187x^4 +604x^3 -33x^2 -972x - 133)/(x-1)^7, {x,0,36}], x]
%t LinearRecurrence[{7,-21,35,-35,21,-7,1}, {133,1903,10561,38015,106461, 252737,533397}, 36]
%t (* End *)
%o (Magma) [(60*n^6 -883*n^5 +3140*n^4 +10775*n^3 -91400*n^2 +171068*n -58020)/60: n in [6..46]]; // _G. C. Greubel_, Jan 03 2024
%o (SageMath) [(60*n^6 -883*n^5 +3140*n^4 +10775*n^3 -91400*n^2 +171068*n -58020)/60 for n in range(6,47)] # _G. C. Greubel_, Jan 03 2024
%Y Cf. A003777, A003878, A028294.
%K nonn,easy
%O 6,1
%A _R. K. Guy_
%E Entry revised by _N. J. A. Sloane_, Jun 15 2014
%E a(17)-a(32) from _Robert G. Wilson v_, Jul 29 2018
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