A164007 Zero together with row 7 of the array in A163280.
0, 13, 26, 33, 52, 55, 78, 91, 112, 135, 160, 187, 216, 247, 280, 315, 352, 391, 432, 475, 520, 567, 616, 667, 720, 775, 832, 891, 952, 1015, 1080, 1147, 1216, 1287, 1360, 1435, 1512, 1591, 1672, 1755, 1840, 1927, 2016, 2107, 2200, 2295, 2392, 2491, 2592, 2695
Offset: 0
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).
Programs
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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: 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
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Mathematica
Join[{0, 13, 26, 33, 52, 55, 78}, Table[n*(n + 6), {n, 7, 50}]] (* G. C. Greubel, Aug 28 2017 *) LinearRecurrence[{3,-3,1},{0,13,26,33,52,55,78,91,112,135},50] (* Harvey P. Dale, Jul 03 2020 *) -
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
Formula
From G. C. Greubel, Aug 28 2017: (Start)
a(n) = n*(n+6), n >= 7.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), n >= 7.
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.
E.g.f.: (7*x + x^2)*exp(x) + 6*x +5*x^2 + x^3 + x^4/2 + x^6/120. (End)
Extensions
Extended by R. J. Mathar, Aug 09 2009