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 A257932 Expansion of 1/(1-x-x^2-x^3+x^5+x^7). 1
 1, 1, 2, 4, 7, 12, 22, 38, 67, 118, 207, 363, 638, 1119, 1964, 3447, 6049, 10615, 18629, 32691, 57369, 100676, 176674, 310041, 544085, 954802, 1675561, 2940405, 5160051, 9055258, 15890871, 27886534, 48937456, 85879249, 150707576, 264473359, 464118392, 814471000, 1429296968 (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) where the position (order) of 3's is unimportant. LINKS Robert Israel, Table of n, a(n) for n = 0..4090 Index entries for linear recurrences with constant coefficients, signature (1,1,1,0,-1,0,-1). FORMULA a(n) = a(n-1) + a(n-2) + a(n-3) - a(n-5) - a(n-7). G.f.: 1 / ((x-1)*(x+1)*(x^2+x+1)*(x^3-x^2+2*x-1)). - Colin Barker, May 17 2015 EXAMPLE a(6)=22; these are (42),(24),(411),(141),(114),(33),(321=231=213),(312=132=123),(3111=1311=1131=1113),(222),(2211),(1122),(1221),(2112),(2121),(1212),(21111),(12111),(11211),(11121),(11112),(111111). MAPLE f:= gfun:-rectoproc({a(n) = a(n-1) + a(n-2) + a(n-3) - a(n-5) - a(n-7), seq(a(i)=[1, 1, 2, 4, 7, 12, 22][i+1], i=0..6)}, a(n), remember): map(f, [\$0..50]); # Robert Israel, Apr 26 2017 MATHEMATICA LinearRecurrence[{1, 1, 1, 0, -1, 0, -1}, {1, 1, 2, 4, 7, 12, 22}, 39] (* Robert P. P. McKone, Feb 08 2021 *) PROG (PARI) Vec(1/((x-1)*(x+1)*(x^2+x+1)*(x^3-x^2+2*x-1)) + O(x^100)) \\ Colin Barker, May 17 2015 CROSSREFS Sequence in context: A309733 A289107 A221944 * A287439 A026713 A288996 Adjacent sequences:  A257929 A257930 A257931 * A257933 A257934 A257935 KEYWORD nonn,easy AUTHOR David Neil McGrath, May 13 2015 STATUS approved

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Last modified May 16 12:30 EDT 2021. Contains 343947 sequences. (Running on oeis4.)