%I #26 Oct 07 2024 06:33:13
%S 0,13,26,33,52,55,78,91,112,135,160,187,216,247,280,315,352,391,432,
%T 475,520,567,616,667,720,775,832,891,952,1015,1080,1147,1216,1287,
%U 1360,1435,1512,1591,1672,1755,1840,1927,2016,2107,2200,2295,2392,2491,2592,2695
%N Zero together with row 7 of the array in A163280.
%H G. C. Greubel, <a href="/A164007/b164007.txt">Table of n, a(n) for n = 0..5000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F From _G. C. Greubel_, Aug 28 2017: (Start)
%F a(n) = n*(n+6), n >= 7.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), n >= 7.
%F G.f.: x*(13 - 13*x - 6*x^2 + 18*x^3 - 28*x^4 + 36*x^5 - 30*x^6 + 18*x^7 - 6*x^8)/(1 - x)^3.
%F E.g.f.: (7*x + x^2)*exp(x) + 6*x +5*x^2 + x^3 + x^4/2 + x^6/120. (End)
%p A033676 := proc(n) local a,d; a := 0 ; for d in numtheory[divisors](n) do if d^2 <= n then a := max(a,d) ; fi; od: a; end: A163280 := proc(n,k) local r,T ; r := 0 ; for T from k^2 by k do if A033676(T) = k then r := r+1 ; if r = n then RETURN(T) ; fi; fi; od: end: A164007 := proc(n) if n = 0 then 0; else A163280(7,n) ; fi; end: seq(A164007(n),n=0..80) ; # _R. J. Mathar_, Aug 09 2009
%t Join[{0, 13, 26, 33, 52, 55, 78}, Table[n*(n + 6), {n, 7, 50}]] (* _G. C. Greubel_, Aug 28 2017 *)
%t LinearRecurrence[{3,-3,1},{0,13,26,33,52,55,78,91,112,135},50] (* _Harvey P. Dale_, Jul 03 2020 *)
%o (PARI) my(x='x+O('x^50)); concat([0], Vec(x*(13 - 13*x - 6*x^2 + 18*x^3 - 28*x^4 + 36*x^5 - 30*x^6 + 18*x^7 - 6*x^8)/(1 - x)^3)) \\ _G. C. Greubel_, Aug 28 2017
%Y Cf. A008578, A161344, A161345, A163280, A164000, A164006, A164008.
%Y Cf. A028560 for n > 6.
%K nonn,easy
%O 0,2
%A _Omar E. Pol_, Aug 08 2009
%E Extended by _R. J. Mathar_, Aug 09 2009