cp's OEIS Frontend

A281857 Numbers occurring in a curious cubic identity.

%I A281857 #35 Aug 27 2024 22:40:31
%S A281857 153,165033,166500333,166650003333,166665000033333,166666500000333333,
%T A281857 166666650000003333333,166666665000000033333333,
%U A281857 166666666500000000333333333,166666666650000000003333333333,166666666665000000000033333333333,166666666666500000000000333333333333
%N A281857 Numbers occurring in a curious cubic identity.
%C A281857 See A246057 for the van der Poorten et al. reference and a comment.
%C A281857 153 is the Armstrong number A005188(10). [Typo corrected by _Jeremy Tan_, Feb 25 2023]
%H A281857 Colin Barker, <a href="/A281857/b281857.txt">Table of n, a(n) for n = 1..333</a>
%H A281857 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1111,-112110,1111000,-1000000).
%F A281857 a(n) = A246057(n-1)^3 + A093143(n)^3 + A002277(n)^3, n >= 1.
%F A281857 From _Colin Barker_, Feb 08 2017: (Start)
%F A281857 G.f.: 9*x*(17 - 550*x + 33500*x^2) / ((1 - x)*(1 - 10*x)*(1 - 100*x)*(1 - 1000*x)).
%F A281857 a(n) = (-2 + 2^(1+n)*5^n - 100^n + 1000^n) / 6.
%F A281857 a(n) = 1111*a(n-1) - 112110*a(n-2) + 1111000*a(n-3) - 1000000*a(n-4) for n>4. (End)
%e A281857 1^3 + 5^3 + 3^3 = 153, 16^3 + 50^3 + 33^3 = 165033, 166^3 + 500^3 + 333^3 = 166500333, ...
%t A281857 Table[FromDigits@ Join[ReplacePart[ConstantArray[6, n], 1 -> 1], ReplacePart[ConstantArray[0, n], 1 -> 5], ConstantArray[3, n]], {n, 12}] (* _Michael De Vlieger_, Feb 08 2017 *)
%o A281857 (PARI) Vec(9*x*(17 - 550*x + 33500*x^2) / ((1 - x)*(1 - 10*x)*(1 - 100*x)*(1 - 1000*x)) + O(x^15)) \\ _Colin Barker_, Feb 08 2017
%o A281857 (PARI) a(n) = (((10^n - 4)/6)^3) + ((10^n/2)^3) + (((10^n - 1)/3)^3) \\ _Jean-Jacques Vaudroz_, Aug 11 2024
%Y A281857 Cf. A002277, A005188, A093143, A246057, A281858, A281859, A281860.
%K A281857 nonn,easy
%O A281857 1,1
%A A281857 _Wolfdieter Lang_, Feb 07 2017