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A281860 Curious identities based on the Armstrong number 371 = A005188(12). 4
371, 336701, 333667001, 333366670001, 333336666700001, 333333666667000001, 333333366666670000001, 333333336666666700000001, 333333333666666667000000001, 333333333366666666670000000001, 333333333336666666666700000000001, 333333333333666666666667000000000001 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
See a comment in A067275.
LINKS
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.
a(n) = A002277(n)^3 + A067275(n+1)^3 + (0(n-1)1)^3.
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.
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
Sequence in context: A037232 A165330 A051182 * A161362 A203924 A004021
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Feb 08 2017
STATUS
approved

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Last modified March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)