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A109242 Expansion of 1/((1-x)(1-10x)(1-100x)). 5
1, 111, 11211, 1122211, 112232211, 11223332211, 1122334332211, 112233444332211, 11223344544332211, 1122334455544332211, 112233445565544332211, 11223344556665544332211 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Partial sums of A109241.

LINKS

Table of n, a(n) for n=0..11.

Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

FORMULA

a(n) = 10^(2n+3)/891 - 10^(n+1)/81 + 1/891;

a(n) = 111a(n-1) - 1110a(n-2) + 1000a(n-3).

a(n) = 110*a(n-1) -1000*a(n-2) + 1, n >= 2. - Vincenzo Librandi, Mar 18 2011

EXAMPLE

The numbers of 1's, 2's, 3's etc. appearing occur according to

1:1,3,4,4,4,4,4,4...

2:0,0,1,3,4,4,4,4...

3:0,0,0,0,1,3,4,4,..

4:0,0,0,0,0,0,1,3,... etc. up to term 17, where 9->10 etc. changes the pattern.

PROG

(Sage) [gaussian_binomial(n, 2, 10) for n in xrange(2, 14)] # Zerinvary Lajos, May 27 2009

CROSSREFS

Sequence in context: A262629 A111864 A098034 * A165155 A078270 A298677

Adjacent sequences:  A109239 A109240 A109241 * A109243 A109244 A109245

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jun 23 2005

STATUS

approved

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Last modified May 25 16:47 EDT 2018. Contains 304567 sequences. (Running on oeis4.)