A074992 a(n) = (10^(2*n)+10^n+1)/3.

1, 37, 3367, 333667, 33336667, 3333366667, 333333666667, 33333336666667, 3333333366666667, 333333333666666667, 33333333336666666667, 3333333333366666666667, 333333333333666666666667, 33333333333336666666666667, 3333333333333366666666666667, 333333333333333666666666666667

Offset

0,2

Comments

Apart from the initial 1, common difference of the arithmetic progression pertaining to the sequence A074991.

This is also a root sequence pertaining to the patterned perfect square sequence 1369, 11336689,111333666889,... i.e., k ones, k threes and k sixes followed by (k-1) 8's and a 9. (37^2 = 1369).

This is a self-complementing sequence: each term has even number of digits (the first one has to be read 01, the leading zero is important). If you add the first half to the second half of any term, you get the sequence A011557, powers of 10. Furthermore, the reciprocals of the sequence terms, except the first one, give a sequence of periodic terms with period sequence as in A008585, a(n)=3n, and value given by A086574, a(n)=k where R(k+3)=3. - Rodolfo A. Fiorini, Jul 14 2016

Links

Table of n, a(n) for n=0..15.

Rodolfo A. Fiorini, Computerized tomography noise reduction by CICT optimized exponential cyclic sequences (OECS) co-domain, Fundamenta Informaticae, 141(2015), 115-134.

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), for n>2, a(0)=1, a(1)=37, a(2)=3367.

G.f.: (1 - 74*x + 370*x^2)/((1-x)(1-10*x)(1-100*x)). - Colin Barker, Sep 23 2013 and Robert Israel, Jul 22 2016

Maple

A074992 := proc(n)
    (10^(2*n)+10^n+1)/3 ;
end proc:
seq(A074992(n), n=0..15) ; # R. J. Mathar, May 06 2017

Mathematica

{01}~Join~Table[FromDigits@ Flatten@ Map[IntegerDigits, {#, 10^n - #}] &@ Floor[10^n/3], {n, 12}] (* Michael De Vlieger, Jul 22 2016 *)

Prog

(PARI) a(n) = (10^(2*n) + 10^n + 1)/3; \\ Michel Marcus, Sep 14 2013
(PARI) Vec(-x*(1000*x^2-740*x+37)/((x-1)*(10*x-1)*(100*x-1)) + O(x^100)) \\ Colin Barker, Sep 23 2013
(PARI) a(n)=my(x=10^n); (x^2+x+1)/3 \\ Charles R Greathouse IV, Jul 22 2016

Crossrefs

Cf. A074991, A011557, A008585, A086574, A274766.

Sequence in context: A141087 A218822 A220385 * A231522 A030095 A334259

Adjacent sequences: A074989 A074990 A074991 * A074993 A074994 A074995

Keyword

nonn,easy

Author

Amarnath Murthy, Aug 31 2002

Extensions

Entry revised (new definition, new offset, new initial term, etc.) by N. J. A. Sloane, Jul 27 2016 (Some of the old programs may need slight modifications.)

Status

approved