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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 Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,-1,-1,-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). 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 Cf. A258000, A257863. Sequence in context: A135491 A164154 A164156 * A258000 A164155 A164167 Adjacent sequences:  A257931 A257932 A257933 * A257935 A257936 A257937 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 November 21 09:56 EST 2019. Contains 329362 sequences. (Running on oeis4.)