A245332 Number of compositions of n into parts 2 and 3 with at least one 2 and one 3.

0, 0, 0, 0, 0, 2, 0, 3, 3, 4, 6, 9, 10, 16, 20, 27, 36, 49, 63, 86, 113, 150, 199, 265, 349, 465, 615, 815, 1080, 1432, 1895, 2513, 3328, 4409, 5841, 7739, 10250, 13581, 17990, 23832, 31571, 41824, 55403, 73396, 97228, 128800, 170624, 226030, 299424, 396655

Offset

0,6

Comments

The g.f. for compositions of n into parts r, s with both parts present is 1 + 1/(1-x^r-x^s) - 1/(1-x^r) - 1/(1-x^s). - Joerg Arndt, Jul 24 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (-1, 1, 3, 2, -1, -2, -1).

Formula

a(n) = a(n-2)+a(n-3)+b(n) with initial terms a(5)=2,a(6)=0,a(7)=3 and b(8)=1,b(9)=1,b(10)=0,b(11)=2,b(12)=0,b(13)=1 and b(n)=b(n-6).

G.f.: x^5*(x^2+2*x+2) / ((x-1)*(x+1)*(x^2+x+1)*(x^3+x^2-1)). - Colin Barker, Jul 18 2014

Example

a(12) = number of rearrangements of 33222 = 5!/(3!*2!) = 10.

Mathematica

CoefficientList[Series[x^5 (x^2 + 2 x + 2)/((x - 1) (x + 1) (x^2 + x + 1) (x^3 + x^2 - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 25 2014 *)

Prog

(PARI) a=vector(100); a[5]=2; a[7]=3; b=[1, 1, 0, 2, 0, 1]; k=1; for(n=8, #a, a[n]=a[n-2]+a[n-3]+b[k]; if(k==6, k=1, k++)); a \\ Colin Barker, Jul 18 2014
(PARI)
x='x+O('x^66);
r=2;  s=3;
gf = 1 + 1/(1-x^r-x^s) - 1/(1-x^r) - 1/(1-x^s);
Vec(gf)
\\ Joerg Arndt, Jul 24 2014

Crossrefs

Sequence in context: A180772 A370594 A291304 * A202035 A369494 A343762

Adjacent sequences: A245329 A245330 A245331 * A245333 A245334 A245335

Keyword

nonn,easy

Author

David Neil McGrath, Jul 18 2014

Extensions

More terms from Colin Barker, Jul 18 2014

Status

approved