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%I #29 Jan 03 2024 04:53:41
%S 1,20,281,1357,4281,10666,22825,43891,77937,130096,206681,315305,
%T 465001,666342,931561,1274671,1711585,2260236,2940697,3775301,4788761,
%U 6008290,7463721,9187627,11215441,13585576,16339545,19522081,23181257,27368606,32139241
%N a(n) = n^5 - (65/6)*n^4 + (173/6)*n^3 + (148/3)*n^2 - (862/3)*n + 265.
%C Old name was: "Number of stacks of n pikelets, distance 5 flips from a well-ordered stack".
%H G. C. Greubel, <a href="/A028294/b028294.txt">Table of n, a(n) for n = 4..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F G.f.: x^4*(1+14*x+176*x^2-49*x^3-31*x^4+9*x^5) / (1-x)^6. - _Colin Barker_, Jun 04 2014
%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). - _Wesley Ivan Hurt_, Aug 28 2015
%F E.g.f.: (x^5 -(5/6)*x^4 - (67/6)*x^3 + 75*x^2 - 219*x + 265)*exp(x) + (3/2)*x^3 + (23/2)*x^2 - 46*x - 265. - _G. C. Greubel_, Aug 29 2015
%p A028294:=n->n^5 - (65/6)*n^4 + (173/6)*n^3 + (148/3)*n^2 - (862/3)*n + 265: seq(A028294(n), n=4..40); # _Wesley Ivan Hurt_, Aug 28 2015
%t CoefficientList[Series[(9*x^5 - 31*x^4 - 49*x^3 + 176*x^2 + 14*x + 1)/(x - 1)^6, {x, 0, 40}], x] (* _Wesley Ivan Hurt_, Aug 28 2015 *)
%t Table[n^5 - (65/6) n^4 + (173/6) n^3 + (148/3) n^2 - (862/3)n + 265, {n, 4, 40}] (* _Vincenzo Librandi_, Aug 29 2015 *)
%t LinearRecurrence[{6,-15,20,-15,6,-1},{1,20,281,1357,4281,10666},40] (* _Harvey P. Dale_, Dec 29 2018 *)
%o (PARI) Vec(x^4*(9*x^5-31*x^4-49*x^3+176*x^2+14*x+1)/(x-1)^6 + O(x^100)) \\ _Colin Barker_, Jun 04 2014
%o (Magma) [n^5 - (65/6)*n^4 + (173/6)*n^3 + (148/3)*n^2 - (862/3)*n + 265 : n in [4..40]]; // _Wesley Ivan Hurt_, Aug 28 2015
%o (Magma) I:=[1,20,281,1357,4281,10666]; [n le 6 select I[n] else 6*Self(n-1)-15*Self(n-2)+20*Self(n-3)-15*Self(n-4)+6*Self(n-5)-Self(n-6): n in [1..40]]; // _Vincenzo Librandi_, Aug 29 2015
%o (SageMath) [(6*n^5 -65*n^4 +173*n^3 +296*n^2 -1724*n +1590)/6 for n in range(4,41)] # _G. C. Greubel_, Jan 03 2024
%K nonn,easy
%O 4,2
%A _R. K. Guy_
%E More terms from _David Wasserman_, Jan 22 2005
%E Entry revised by _N. J. A. Sloane_, Jun 15 2014
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