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%I #20 Oct 21 2022 21:04:26
%S 1,23,60,122,217,354,543,795,1122,1537,2054,2688,3455,4372,5457,6729,
%T 8208,9915,11872,14102,16629,19478,22675,26247,30222,34629,39498,
%U 44860,50747,57192,64229,71893,80220,89247,99012,109554,120913,133130,146247,160307,175354
%N a(n) = T(n,n-4), array T as in A055818.
%H Vincenzo Librandi, <a href="/A055821/b055821.txt">Table of n, a(n) for n = 4..5000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F From _Chai Wah Wu_, Dec 29 2016: (Start)
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 9.
%F G.f.: x^4*(1 + 18*x - 45*x^2 + 42*x^3 - 18*x^4 + 3*x^5)/(1-x)^5. (End)
%F From _G. C. Greubel_, Jan 22 2020: (Start)
%F a(n) = (72 - 54*n - 25*n^2 + 6*n^3 + n^4)/24 for n > 4, with a(4) = 1.
%F E.g.f.: (-72 +36*x^2 -3*x^4 + (72 - 72*x + 12*x^3 + x^4)*exp(x))/24. (End)
%p seq( `if`(n=4, 1, (72 -54*n -25*n^2 +6*n^3 +n^4)/24), n=4..50); # _G. C. Greubel_, Jan 22 2020
%t Join[{1, 23, 60, 122}, LinearRecurrence[{5,-10,10,-5,1}, {217,354,543,795, 1122}, 45]] (* _Vincenzo Librandi_, Dec 30 2016 *)
%t Table[If[n==4, 1, (72 -54*n -25*n^2 +6*n^3 +n^4)/24], {n,4,50}] (* _G. C. Greubel_, Jan 22 2020 *)
%o (Magma) I:=[1,23,60,122,217,354,543,795,1122]; [n le 9 select I[n] else 5*Self(n-1)-10*Self(n-2)+10*Self(n-3)- 5*Self(n-4)+Self(n-5): n in [1..50]]; // _Vincenzo Librandi_, Dec 30 2016
%o (PARI) vector(50, n, my(m=n+3); if(m==4, 1, (72 -54*m -25*m^2 +6*m^3 +m^4)/24)) \\ _G. C. Greubel_, Jan 22 2020
%o (Sage) [1]+[(72 -54*n -25*n^2 +6*n^3 +n^4)/24 for n in (5..50)] # _G. C. Greubel_, Jan 22 2020
%o (GAP) Concatenation([1], List([5..50], n-> (72 -54*n -25*n^2 +6*n^3 +n^4)/24 )); # _G. C. Greubel_, Jan 22 2020
%Y Cf. A055818.
%K nonn,easy
%O 4,2
%A _Clark Kimberling_, May 28 2000
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