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

0,2

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).

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)

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

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 *)

Prog

(PARI) 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

Crossrefs

Cf. A008578, A161344, A161345, A163280, A164000, A164006, A164008.

Cf. A028560 for n > 6.

Sequence in context: A180055 A371463 A346003 * A101870 A321714 A260748

Adjacent sequences: A164004 A164005 A164006 * A164008 A164009 A164010

Keyword

nonn,easy

Author

Omar E. Pol, Aug 08 2009

Extensions

Extended by R. J. Mathar, Aug 09 2009

Status

approved