A164004 Zero together with row 4 of the array in A163280.

0, 5, 10, 18, 28, 40, 54, 70, 88, 108, 130, 154, 180, 208, 238, 270, 304, 340, 378, 418, 460, 504, 550, 598, 648, 700, 754, 810, 868, 928, 990, 1054, 1120, 1188, 1258, 1330, 1404, 1480, 1558, 1638, 1720, 1804, 1890, 1978, 2068, 2160, 2254, 2350, 2448, 2548

Offset: 0

Author

Omar E. Pol, Aug 08 2009

Keywords

• nonn
• easy
• less

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).

Crossrefs

Cf. A008578, A161344, A161345, A163280, A164000, A005563, A164005.

Cf. A028552.

Programs

Maple

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: A164004 := proc(n) if n = 0 then 0; else A163280(4,n) ; fi; end: seq(A164004(n),n=0..80) ; # R. J. Mathar, Aug 09 2009

Mathematica

Join[{0, 5}, Table[n*(n + 3), {n, 2, 50}]] (* G. C. Greubel, Aug 28 2017 *)

PARI

x='x+O('x^50); concat([0], Vec(x*(x^3 -3*x^2 +5*x -5)/(x-1)^3)) \\ G. C. Greubel, Aug 28 2017

Formula

Conjectures from Colin Barker, Apr 07 2015: (Start)

a(n) = n*(3+n) = A028552(n) for n > 1.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 4.

G.f.: x*(x^3 - 3*x^2 + 5*x - 5) / (x-1)^3. (End)

E.g.f.: x*(x+4)*exp(x) + x. - G. C. Greubel, Aug 28 2017

Extensions

Extended beyond a(12) by R. J. Mathar, Aug 09 2009