A257932 Expansion of 1/(1-x-x^2-x^3+x^5+x^7).

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.

Links

Robert Israel, Table of n, a(n) for n = 0..4090

Index entries for related partition-counting sequences

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