A140953 Expansion of 1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^7)*(1-x^11)*(1-x^13)).

1, 0, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 9, 10, 12, 14, 16, 19, 21, 25, 28, 32, 36, 41, 46, 52, 58, 65, 72, 80, 89, 98, 109, 119, 132, 144, 158, 173, 189, 206, 224, 244, 264, 287, 310, 336, 362, 391, 421, 453, 487, 523, 561, 601, 644, 688, 736, 785, 838, 893

Offset: 0

Author

Alois P. Heinz, Jul 25 2008

Keywords

• nonn
• easy

Comments

Number of partitions of n into the first 6 primes. [Corrected by Harvey P. Dale, Dec 05 2022]

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (0,1,1,0, 0,0,0,-1,-1,0,1,0,0,0,0,-1,-1,0,1,1,1,1,0,-1,-1,0,0,0,0,1,0,-1,-1,0,0,0,0,1,1,0,-1).

Crossrefs

Cf. A000040, A025795, A029144, A103221, A140952, A335106.

Programs

Maple

M := Matrix(41, (i,j)-> if (i=j-1) or (j=1 and member(i, [2, 3, 11, 19, 20, 21, 22, 30, 38, 39])) then 1 elif j=1 and member(i, [8, 9, 16, 17, 24, 25, 32, 33, 41]) then -1 else 0 fi):
a:= n -> (M^(n))[1,1]:
seq(a(n), n=0..50);

Mathematica

CoefficientList[Series[1/Times@@Table[1-x^p,{p,Prime[Range[6]]}],{x,0,60}],x] (* or *) LinearRecurrence[{0,1,1,0,0,0,0,-1,-1,0,1,0,0,0,0,-1,-1,0,1,1,1,1,0,-1,-1,0,0,0,0,1,0,-1,-1,0,0,0,0,1,1,0,-1},{1,0,1,1,1,2,2,3,3,4,5,6,7,9,10,12,14,16,19,21,25,28,32,36,41,46,52,58,65,72,80,89,98,109,119,132,144,158,173,189,206},70] (* Harvey P. Dale, Dec 05 2022 *)