OFFSET
0,2
COMMENTS
a(k-1) = (10^k - 4)/6, together with b(k) = 3*a(k-1) + 2 = A093143(k) and c(k) = 2*a(k-1) + 1 = A002277(k) are k-digit numbers for k >= 1 satisfying the so-called curious cubic identity a(k-1)^3 + b(k)^3 + c(k)^3 = a(k)*10^(2*k) + b(k)*10^k + c(k) (concatenated a(k)b(k)c(k)). This k-family and the proof of the identity has been given in the introduction of the van der Poorten reference. Thanks go to S. Heinemeyer for bringing these identities to my attention. - Wolfdieter Lang, Feb 07 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..100
A. van der Poorten, K. Thomsen, and M. Wiebe, A curious cubic identity and self-similar sums of squares, The Mathematical Intelligencer, v.29(2), pp. 39-41, March 2007.
Index entries for linear recurrences with constant coefficients, signature (11,-10).
FORMULA
G.f.: (1 + 5*x)/((1 - x)*(1 - 10*x)).
a(n) = 11*a(n-1) - 10*a(n-2).
EXAMPLE
Curious cubic identities (see a comment and reference above): 1^3 + 5^3 + 3^3 = 153, 16^3 + 50^3 + 33^3 = 165033, 166^3 + 500^3 + 333^3 = 166500333, ... - Wolfdieter Lang, Feb 07 2017
MATHEMATICA
Table[(5 10^n - 2)/3, {n, 0, 20}]
PROG
(Magma) [(5*10^n-2)/3: n in [0..20]];
(PARI) vector(50, n, (5*10^(n-1)-2)/3) \\ Derek Orr, Aug 13 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Aug 13 2014
STATUS
approved