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%I #16 Mar 08 2023 14:53:20
%S 1,1,1,2,3,5,8,13,20,32,46,72,97,148,189,281,344,499,591,838,967,1343,
%T 1518,2069,2300,3082,3380,4460,4837,6294,6763,8689,9264,11765,12461,
%U 15658,16491,20521,21508,26525,27684,33860
%N a(n) = T(n,n-5), array T as in A055801.
%H G. C. Greubel, <a href="/A055805/b055805.txt">Table of n, a(n) for n = 5..1000</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1,5,-5,-10,10,10,-10,-5,5,1,-1).
%F From _Colin Barker_, Nov 28 2014: (Start)
%F a(n) = ((2*n^5 -45*n^4 +450*n^3 -2070*n^2 +4873*n -3585) +5*(-1)^n*(n^4 -34*n^3 +446*n^2 -2741*n +6861))/7680 for n>5.
%F G.f.: x^5*(1 -5*x^2 +x^3 +11*x^4 -3*x^5 -12*x^6 +5*x^7 +7*x^8 -3*x^9 -2*x^10 + x^11)/((1-x)^6*(1+x)^5). (End)
%p seq( `if`(n=5, 1, ((2*n^5 -45*n^4 +450*n^3 -2070*n^2 +4873*n -3585) +5*(-1)^n*(n^4 -34*n^3 +446*n^2 -2741*n +6861))/7680), n=5..50); # _G. C. Greubel_, Jan 24 2020
%t Table[If[n==5, 1, ((2*n^5 -45*n^4 +450*n^3 -2070*n^2 +4873*n -3585) +5*(-1)^n*(n^4 -34*n^3 +446*n^2 -2741*n +6861))/7680], {n,5,50}] (* _G. C. Greubel_, Jan 24 2020 *)
%t LinearRecurrence[{1,5,-5,-10,10,10,-10,-5,5,1,-1},{1,1,1,2,3,5,8,13,20,32,46,72},50] (* _Harvey P. Dale_, Mar 08 2023 *)
%o (PARI) vector(50, n, my(m=n+4); if(m==5, 1, ((2*m^5 -45*m^4 +450*m^3 -2070*m^2 +4873*m -3585) +5*(-1)^m*(m^4 -34*m^3 +446*m^2 -2741*m +6861))/7680)) \\ _G. C. Greubel_, Jan 24 2020
%o (Magma) [1] cat [((2*n^5 -45*n^4 +450*n^3 -2070*n^2 +4873*n -3585) +5*(-1)^n*(n^4 -34*n^3 +446*n^2 -2741*n +6861))/7680: n in [6..50]]; // _G. C. Greubel_, Jan 24 2020
%o (Sage) [1]+[((2*n^5 -45*n^4 +450*n^3 -2070*n^2 +4873*n -3585) +5*(-1)^n*(n^4 -34*n^3 +446*n^2 -2741*n +6861))/7680 for n in (6..50)] # _G. C. Greubel_, Jan 24 2020
%o (GAP) Concatenation([1], List([6..50], n-> ((2*n^5 -45*n^4 +450*n^3 -2070*n^2 +4873*n -3585) +5*(-1)^n*(n^4 -34*n^3 +446*n^2 -2741*n +6861))/7680 )); # _G. C. Greubel_, Jan 24 2020
%Y Cf. A055801, A055802, A055803, A055804, A055806.
%K nonn
%O 5,4
%A _Clark Kimberling_, May 28 2000
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