A140952 Expansion of 1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^7)*(1-x^11)).

1, 0, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 8, 10, 11, 13, 15, 17, 19, 22, 25, 28, 31, 35, 39, 43, 48, 53, 58, 64, 70, 77, 84, 91, 100, 108, 117, 127, 137, 148, 159, 172, 184, 198, 212, 227, 243, 259, 277, 295, 314, 334, 355, 377, 400, 424, 449, 475, 502, 531, 560

Offset

0,6

Comments

Number of partitions of n into the first 5 primes.

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,-1,0,1,0,-1,0,1,1,0,0,0,0,-1,-1,0,1).

Maple

M := Matrix(28, (i, j)-> if (i=j-1) or (j=1 and member(i, [2, 3, 11, 15, 19, 20, 28])) then 1 elif j=1 and member(i, [8, 9, 13, 17, 25, 26]) then -1 else 0 fi):
a:= n-> (M^(n))[1, 1]:
seq(a(n), n=0..50);

Mathematica

CoefficientList[Series[1/Times@@(1-x^Prime[Range[5]]), {x, 0, 70}], x] (* or *) LinearRecurrence[{0, 1, 1, 0, 0, 0, 0, -1, -1, 0, 1, 0, -1, 0, 1, 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, 8, 10, 11, 13, 15, 17, 19, 22, 25, 28, 31, 35, 39, 43, 48}, 70] (* Harvey P. Dale, Jun 18 2021 *)

Crossrefs

Cf. A000040, A025795, A029144, A103221, A140953, A335106.

Sequence in context: A358637 A106244 A029023 * A096911 A143752 A145933

Adjacent sequences: A140949 A140950 A140951 * A140953 A140954 A140955

Keyword

nonn,easy

Author

Alois P. Heinz, Jul 25 2008

Status

approved