cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A281858 Curious cubic identities based on the Armstrong number 370.

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%I A281858 #28 Apr 07 2020 20:47:25
%S A281858 370,336700,333667000,333366670000,333336666700000,333333666667000000,
%T A281858 333333366666670000000,333333336666666700000000,
%U A281858 333333333666666667000000000,333333333366666666670000000000,333333333336666666666700000000000,333333333333666666666667000000000000
%N A281858 Curious cubic identities based on the Armstrong number 370.
%C A281858 See a comment in A067275, and the analog to the Armstrong number 153 = A005188(10) treated in A281857, 370 = A005188(11).
%H A281858 Colin Barker, <a href="/A281858/b281858.txt">Table of n, a(n) for n = 1..333</a>
%H A281858 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1110,-111000,1000000).
%F A281858 a(n) = A002277(n)^3 + A067275(n+1)^3 + 0(n)^3, n >= 1, with 0(n) standing for n 0's.
%F A281858 From _Colin Barker_, Feb 08 2017: (Start)
%F A281858 G.f.: 10*x*(37 - 7400*x + 100000*x^2) / ((1 - 10*x)*(1 - 100*x)*(1 - 1000*x)).
%F A281858 a(n) = 10^n*(1 + 10^n + 100^n) / 3.
%F A281858 a(n) = 1110*a(n-1) - 111000*a(n-2) + 1000000*a(n-3) for n>3. (End)
%e A281858 n=1: 370 =  3^3 + 7^3 + 0^3; n=2: 336700 = 33^3 + 67^3 + (00)^3; n=3: 333667000 = 333^3 + 667^3 + (000)^3.
%t A281858 Table[FromDigits@ Join[ConstantArray[3, n], ReplacePart[ConstantArray[6, n], -1 -> 7], ConstantArray[0, n]], {n, 12}] (* _Michael De Vlieger_, Feb 08 2017 *)
%o A281858 (PARI) Vec(10*x*(37 - 7400*x + 100000*x^2) / ((1 - 10*x)*(1 - 100*x)*(1 - 1000*x)) + O(x^30)) \\ _Colin Barker_, Feb 08 2017
%Y A281858 Cf. A002277, A005188, A067275, A246057, A281857.
%K A281858 nonn,easy
%O A281858 1,1
%A A281858 _Wolfdieter Lang_, Feb 08 2017