OFFSET
0,1
COMMENTS
Subsequence of A186074.
Terms of this sequence satisfy the identity proposed in 2nd formula because a(n) = Sum_{j=(4*10^n-1)/3..(16*10^n-1)/3} j = ((4*10^n-1)/3).((16*10^n-1)/3) where "." means concatenation (see examples).
LINKS
Diophante, A1945 - Concaténations en tous genres (in French).
Richard Hoshino, Astonishing Pairs of Numbers, Crux Mathematicorum with Mathematical Mayhem 27:1 (2001), pp. 39-44.
Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).
FORMULA
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3), n >= 3.
G.f.: (15 - 312*x)/((1 - x)*(1 - 10*x)*(1 - 100*x)). - Stefano Spezia, Jan 30 2022
a(n) = 2*A332167(n) + 1. - Hugo Pfoertner, Jan 30 2022
EXAMPLE
a(0) = (40+6-1)/3 = Sum_{j=1..5} j = 15.
a(1) = (4000+60-1)/3 = Sum_{j=13..53} j = 1353.
a(2) = (400000+600-1)/3 = Sum_{j=133..533} j = 133533.
MAPLE
Data := seq((40*100^n + 6*10^n - 1)/3, n = 0..17);
MATHEMATICA
Table[(40*100^n + 6*10^n - 1)/3, {n, 0, 17}] (* Amiram Eldar, Jan 29 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bernard Schott, Jan 28 2022
STATUS
approved