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A109242
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Expansion of 1/((1-x)(1-10x)(1-100x)).
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7
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1, 111, 11211, 1122211, 112232211, 11223332211, 1122334332211, 112233444332211, 11223344544332211, 1122334455544332211, 112233445565544332211, 11223344556665544332211, 1122334455667665544332211, 112233445566777665544332211, 11223344556677877665544332211
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = 10^(2*n+3)/891 - 10^(n+1)/81 + 1/891.
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3).
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EXAMPLE
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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.
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PROG
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(Sage) [gaussian_binomial(n, 2, 10) for n in range(2, 14)] # Zerinvary Lajos, May 27 2009
(PARI) a(n) = {10^(2*n+3)/891 - 10^(n+1)/81 + 1/891} \\ Andrew Howroyd, Nov 08 2019
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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