OFFSET
1,1
COMMENTS
See a comment in A067275.
LINKS
Colin Barker, Table of n, a(n) for n = 1..333
Index entries for linear recurrences with constant coefficients, signature (1111,-112110,1111000,-1000000).
FORMULA
a(n) = A002277(n) * 10^(2*n) + A067275(n+1) * 10^n + 0(n-1)1, where 0(n-1)1 stands for n-1 0's followed by a 1, for n >= 1.
From Colin Barker, Feb 09 2017: (Start)
G.f.: x*(371 - 75480*x + 1185000*x^2 - 2000000*x^3)/((1 - x)*(1 - 10*x)*(1 - 100*x)*(1 - 1000*x)).
a(n) = 1111*a(n-1) - 112110*a(n-2) + 1111000*a(n-3) - 1000000*a(n-4) for n>4.
a(n) = (3 + 10^n + 100^n + 1000^n)/3. (End)
EXAMPLE
n=1: 371 = 3^3 + 7^3 + 1^3;
n=2: 336701 = 33^3 + 67^3 + (01)^3;
n=3: 333667001 = 333^3 + 667^3 + (001)^3.
MATHEMATICA
LinearRecurrence[{1111, -112110, 1111000, -1000000}, {371, 336701, 333667001, 333366670001}, 20] (* Harvey P. Dale, May 28 2024 *)
PROG
(PARI) Vec(x*(371 - 75480*x + 1185000*x^2 - 2000000*x^3) / ((1 - x)*(1 - 10*x)*(1 - 100*x)*(1 - 1000*x)) + O(x^30)) \\ Colin Barker, Feb 09 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Feb 08 2017
STATUS
approved