A164005 - OEIS

%I #16 Jan 25 2023 06:47:21

%S 0,7,14,21,32,45,60,77,96,117,140,165,192,221,252,285,320,357,396,437,

%T 480,525,572,621,672,725,780,837,896,957,1020,1085,1152,1221,1292,

%U 1365,1440,1517,1596,1677,1760,1845,1932,2021,2112,2205,2300,2397,2496,2597

%N Zero together with row 5 of the array in A163280.

%H G. C. Greubel, <a href="/A164005/b164005.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 Conjecture: a(n) = A100451(n+2). (See A163280.)

%F From _G. C. Greubel_, Aug 28 2017: (Start)

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), n >= 3.

%F a(n) = n*(n+4), n >= 3.

%F G.f.: x*(7 - 7*x + 4*x^3 - 2*x^4)/(1 - x)^3.

%F E.g.f.: x*(x+5)*exp(x) + 2*x + x^2. (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: A164005 := proc(n) if n = 0 then 0; else A163280(5,n) ; fi; end: seq(A164005(n),n=0..80) ; # _R. J. Mathar_, Aug 09 2009

%t Join[{0, 7, 14}, Table[n*(n + 4), {n, 3, 50}]] (* _G. C. Greubel_, Aug 28 2017 *)

%o (PARI) x='x+O('x^50); concat([0], Vec(x*(7 - 7*x + 4*x^3 - 2*x^4)/(1 - x)^3)) \\ _G. C. Greubel_, Aug 28 2017

%Y Cf. A008578, A161344, A161345, A163280, A164000, A164004, A164006.

%Y Cf. A028347.

%K nonn,easy

%O 0,2

%A _Omar E. Pol_, Aug 08 2009

%E Extended by _R. J. Mathar_, Aug 09 2009