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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
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.
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
KEYWORD
nonn,easy
AUTHOR
David Neil McGrath, May 16 2015
EXTENSIONS
More terms from Vincenzo Librandi, May 19 2015
STATUS
approved