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 A109242 Expansion of 1/((1-x)(1-10x)(1-100x)). 3
 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 Index to sequences with 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)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 27 2009] CROSSREFS Sequence in context: A100706 A111864 A098034 * A165155 A078270 A172175 Adjacent sequences:  A109239 A109240 A109241 * A109243 A109244 A109245 KEYWORD easy,nonn AUTHOR Paul Barry, Jun 23 2005 STATUS approved

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