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 A258000 Expansion of 1/(1-x-x^2-x^3-x^4+x^5+x^6+x^7-x^9). 1
 1, 1, 2, 4, 8, 14, 26, 48, 89, 164, 302, 557, 1028, 1896, 3496, 6448, 11893, 21935, 40455, 74613, 137613, 253807, 468108, 863354, 1592327, 2936808, 5416499, 9989915, 18424893, 33981939, 62674564, 115593785, 213195313, 393206621, 725210344, 1337541166 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS This sequence counts partially ordered partitions of (n) into parts (1,2,3,4) in which only the position (order) of the 1's are important. The 1's behave as placeholders for unordered 2's,3's and 4's. LINKS Table of n, a(n) for n=0..35. Index entries for partition-counting sequences Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,-1,-1,-1,0,1) FORMULA a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) - a(n-5) - a(n-6) - a(n-7) + a(n-9) G.f.: 1/(1-x-x^2-x^3-x^4+x^5+x^6+x^7-x^9). EXAMPLE a(6)=26; these are (42,24=one),(411),(141),(114),(33),(321,231=one),(123,132=one),(312),(213),(3111=four),(222),(2211),(1122),(2112),(1221),(1212),(2121),(21111=five),(111111). MATHEMATICA LinearRecurrence[{1, 1, 1, 1, -1, -1, -1, 0, 1}, {1, 1, 2, 4, 8, 14, 26, 48, 89}, 50] (* Vincenzo Librandi, May 19 2015 *) PROG (PARI) Vec(1/(-x^9+x^7+x^6+x^5-x^4-x^3-x^2-x+1) + O(x^100)) \\ Colin Barker, May 17 2015 (Magma) I:=[1, 1, 2, 4, 8, 14, 26, 48, 89]; [n le 9 select I[n] else Self(n-1)+Self(n-2)+Self(n-3)+Self(n-4)-Self(n-5)-Self(n-6)-Self(n-7)+Self(n-9): n in [1..40]]; // Vincenzo Librandi, May 19 2015 CROSSREFS Sequence in context: A164154 A164156 A257934 * A164155 A164167 A164169 Adjacent sequences: A257997 A257998 A257999 * A258001 A258002 A258003 KEYWORD nonn,easy AUTHOR David Neil McGrath, May 16 2015 EXTENSIONS More terms from Vincenzo Librandi, May 19 2015 STATUS approved

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Last modified August 2 22:39 EDT 2024. Contains 374875 sequences. (Running on oeis4.)