OFFSET
0,2
COMMENTS
Partial sums of (1+2x)/(1-10x)={1,12,120,1200,...}.
Second binomial transform of A082365.
These terms are the x's of A070152 and the corresponding y's are A350995 (see formula and examples) - Bernard Schott, Feb 15 2022
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
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 (11,-10).
FORMULA
a(n) = (4*10^n - 1)/3.
a(n) = A097169(2n).
a(n) = 10*a(n-1)+3, n>0. a(n) = 11*a(n-1)-10*a(n-2), n>1. - Vincenzo Librandi, Nov 01 2011
A350994(n) = Sum_{j=a(n)..A350995(n)} = a(n).A350995(n) where "." means concatenation. - Bernard Schott, Jan 28 2022
EXAMPLE
a(0) = (4-1)/3 = 1 and Sum_{j=1..5} = 15.
a(1) = (40-1)/3 = 13 and Sum_{j=13..53} = 1353.
a(2) = (400-1)/3 = 133 and Sum_{j=133..533} = 133533.
MAPLE
a:= n-> parse(cat(1, 3$n)):
seq(a(n), n=0..18); # Alois P. Heinz, Aug 23 2019
MATHEMATICA
NestList[10#+3&, 1, 20] (* Harvey P. Dale, Jan 22 2014 *)
PROG
(Magma) [(4*10^n-1)/3 : n in [0..20]]; // Vincenzo Librandi, Nov 01 2011
(Python) [(4*10**n-1)//3 for n in range(25)] # Gennady Eremin, Mar 04 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Jul 30 2004
STATUS
approved