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A257934 Expansion of 1/(1-x-x^2-x^3-x^4+x^5+x^6+x^7). 0
1, 1, 2, 4, 8, 14, 26, 48, 89, 163, 300, 552, 1016, 1868, 3436, 6320, 11625, 21381, 39326, 72332, 133040, 244698, 450070, 827808, 1522577, 2800455, 5150840, 9473872, 17425168, 32049880, 58948920, 108423968, 199422769, 366795657, 674642394, 1240860820, 2282298872, 4197802086, 7720961778 (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 the position (order) of the 4's are unimportant. For example the permutations of (43421) are counted as permutations of (321)=6.
LINKS
FORMULA
a(n)= a(n-1) + a(n-2) + a(n-3) + a(n-4) - a(n-5) - a(n-6) - a(n-7).
G.f.: 1 / ((x-1)*(x+1)*(x^2+1)*(x^3+x^2+x-1)). - Colin Barker, May 17 2015
EXAMPLE
a(6)=26; these are (42=24),(411=141=114),(33),(321=six),(3111=four),(222),(2211=six),(21111=five),(111111).
PROG
(PARI) Vec(1 / ((x-1)*(x+1)*(x^2+1)*(x^3+x^2+x-1)) + O(x^100)) \\ Colin Barker, May 17 2015
CROSSREFS
Sequence in context: A135491 A164154 A164156 * A258000 A164155 A164167
KEYWORD
nonn,easy
AUTHOR
David Neil McGrath, May 13 2015
EXTENSIONS
Missing term (6320) inserted by Colin Barker, May 17 2015
STATUS
approved

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)