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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
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.
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
KEYWORD
nonn,easy
AUTHOR
David Neil McGrath, May 13 2015
STATUS
approved