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%I #13 Sep 08 2022 08:45:01
%S 1,1,1,2,3,5,8,12,19,26,40,51,76,92,133,155,218,247,339,376,505,551,
%T 726,782,1013,1080,1378,1457,1834,1926,2395,2501,3076,3197,3893,4030,
%U 4863,5017,6004,6176,7335,7526,8876,9087
%N a(n) = T(n,n-4), array T as in A055801.
%H G. C. Greubel, <a href="/A055804/b055804.txt">Table of n, a(n) for n = 4..1000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,-4,-6,6,4,-4,-1,1).
%F G.f.: x^4*(-1 +4*x^2 -x^3 -7*x^4 +2*x^5 +5*x^6 -2*x^7 -2*x^8 +x^9)/((1-x)^5 (1+x)^4). - _R. J. Mathar_, Jul 10 2012
%F From _G. C. Greubel_, Jan 24 2020: (Start)
%F a(n) = (2*n^4 -28*n^3 +178*n^2 -416*n +441 +(-1)^n*(4*n^3 -90*n^2 + 704*n -1977))/768 for n>4, with a(4) = 1.
%F E.g.f.: ( (768 -768*x +192*x^2 -64*x^3 +16*x^4) +(-768 -441*x +15*x^2 -10*x^3 +x^4)*cosh(x) +(1209 +177*x +93*x^2 -6*x^3 +x^4)*sinh(x) )/384. (End)
%p seq( `if`(n=4, 1, (2*n^4 -28*n^3 +178*n^2 -416*n +441 +(-1)^n*(4*n^3 -90*n^2 + 704*n -1977))/768), n=4..50); # _G. C. Greubel_, Jan 24 2020
%t Table[If[n==4, 1, (2*n^4 -28*n^3 +178*n^2 -416*n +441 +(-1)^n*(4*n^3 -90*n^2 + 704*n -1977))/768], {n,4,50}] (* _G. C. Greubel_, Jan 24 2020 *)
%o (PARI) vector(50, n, my(m=n+3); if(m==4, 1, (2*m^4 -28*m^3 +178*m^2 -416*m +441 +(-1)^m*(4*m^3 -90*m^2 + 704*m -1977))/768)) \\ _G. C. Greubel_, Jan 24 2020
%o (Magma) [1] cat [(2*n^4 -28*n^3 +178*n^2 -416*n +441 +(-1)^n*(4*n^3 -90*n^2 + 704*n -1977))/768: n in [5..50]]; // _G. C. Greubel_, Jan 24 2020
%o (Sage) [1]+[(2*n^4 -28*n^3 +178*n^2 -416*n +441 +(-1)^n*(4*n^3 -90*n^2 + 704*n -1977))/768 for n in (5..50)] # _G. C. Greubel_, Jan 24 2020
%o (GAP) Concatenation([1], List([5..50], n-> (2*n^4 -28*n^3 +178*n^2 -416*n +441 +(-1)^n*(4*n^3 -90*n^2 + 704*n -1977))/768 )); # _G. C. Greubel_, Jan 24 2020
%Y Cf. A055801, A055802, A055803, A055805, A055806.
%K nonn
%O 4,4
%A _Clark Kimberling_, May 28 2000
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