A055806 - OEIS

%I #8 Sep 08 2022 08:45:01

%S 1,1,1,2,3,5,8,13,21,33,53,79,125,176,273,365,554,709,1053,1300,1891,

%T 2267,3234,3785,5303,6085,8385,9465,12845,14302,19139,21065,27828,

%U 30329,39593,42790,55251,59281,75772

%N a(n) = T(n,n-6), array T as in A055801.

%H G. C. Greubel, <a href="/A055806/b055806.txt">Table of n, a(n) for n = 6..1000</a>

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,6,-6,-15,15,20,-20,-15,15,6,-6,-1,1).

%F From _G. C. Greubel_, Jan 24 2020: (Start)

%F a(n) = (48915 -58884*n +29723*n^2 -7200*n^3 +965*n^4 -66*n^5 +2*n^6 + 3*(-1)^n*(-231345 +98988*n -18505*n^2 +1840*n^3 -95*n^4 +2*n^5))/92160, n > 6.

%F G.f.: x^6*(1 -6*x^2 +x^3 +16*x^4 -4*x^5 -23*x^6 +8*x^7 +20*x^8 -8*x^9 -9*x^10 + 4*x^11 +2*x^12 -x^13)/((1-x)^7*(1+x)^6). (end)

%p seq( `if(n=6,1, (48915 -58884*n +29723*n^2 -7200*n^3 +965*n^4 -66*n^5 +2*n^6 + 3*(-1)^n*(-231345 +98988*n -18505*n^2 +1840*n^3 -95*n^4 +2*n^5))/92160), n=6..50); # _G. C. Greubel_, Jan 24 2020

%t Table[If[n==6, 1, (48915 -58884*n +29723*n^2 -7200*n^3 +965*n^4 -66*n^5 +2*n^6 + 3*(-1)^n*(-231345 +98988*n -18505*n^2 +1840*n^3 -95*n^4 +2*n^5))/92160], {n, 6,50}] (* _G. C. Greubel_, Jan 24 2020 *)

%o (PARI) vector(50, n, my(m=n+5); if(m==6, 1, (48915 -58884*m +29723*m^2 -7200*m^3 +965*m^4 -66*m^5 +2*m^6 + 3*(-1)^m*(-231345 +98988*m -18505*m^2 +1840*m^3 -95*m^4 +2*m^5))/92160)) \\ _G. C. Greubel_, Jan 24 2020

%o (Magma) [1] cat [(48915 -58884*n +29723*n^2 -7200*n^3 +965*n^4 -66*n^5 +2*n^6 + 3*(-1)^n*(-231345 +98988*n -18505*n^2 +1840*n^3 -95*n^4 +2*n^5))/92160: n in [7..50]]; // _G. C. Greubel_, Jan 24 2020

%o (Sage) [1]+[(48915 -58884*n +29723*n^2 -7200*n^3 +965*n^4 -66*n^5 +2*n^6 + 3*(-1)^n*(-231345 +98988*n -18505*n^2 +1840*n^3 -95*n^4 +2*n^5))/92160 for n in (7..50)] # _G. C. Greubel_, Jan 24 2020

%o (GAP) Concatenation([1], List([7..50], n-> (48915 -58884*n +29723*n^2 -7200*n^3 +965*n^4 -66*n^5 +2*n^6 + 3*(-1)^n*(-231345 +98988*n -18505*n^2 +1840*n^3 -95*n^4 +2*n^5))/92160 )); # _G. C. Greubel_, Jan 24 2020

%Y Cf. A055801, A055802, A055803, A055804, A055805.

%K nonn

%O 6,4

%A _Clark Kimberling_, May 28 2000