A064349 Generating function: 1/((1-x)*(1-x^2)^2*(1-x^3)^3*(1-x^4)^4).

1, 1, 3, 6, 13, 19, 37, 58, 97, 143, 227, 328, 492, 688, 992, 1364, 1903, 2551, 3473, 4586, 6097, 7911, 10333, 13226, 16988, 21454, 27172, 33938, 42437, 52423, 64833, 79354, 97130, 117824, 142930, 172018, 206925, 247179, 295105, 350154, 415124

Offset: 0

Author

Henry Bottomley, Sep 17 2001

Keywords

• nonn

Comments

Number of partitions of n into parts 1 (of one kind), 2 (of two kinds), 3 (of three kinds), and 4 (of 4 kinds). [Joerg Arndt, Jul 11 2013]

Links

• Ray Chandler, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1, 2, 1, 0, -9, -5, 2, 13, 21, -4, -17, -30, -13, 25, 28, 25, -13, -30, -17, -4, 21, 13, 2, -5, -9, 0, 1, 2, 1, -1).

Crossrefs

The sequence of sequences A000007, A000012, A008805, A002597, A064349, etc. approaches A000219.

Essentially the same as A002598.

Cf. A002598.

Programs

PARI

a(n) = floor( ([13, 28, -44][n%3+1]+(9/2)*(n\3+2)*((n+1)%3-1)) * (n\3+1)/729 - (n\2+1)*(-1)^(n\2) * (3*[-8, 11]+(n\2+2)*(2*[-1, 3]+(n\2+3)*(1/3)*[0, 1]))[n%2+1]/512 + (2*n^9 +270*n^8 +15600*n^7 +504000*n^6 +9977730*n^5 [phone]*n^4 [phone]*n^3 [phone]*n^2 [phone]*n [phone] +5103*(n+15)*(2*n^4 +120*n^3 +2440*n^2 +19200*n +48213)*(-1)^n) / 20065812480 ) \\ Tani Akinari, Jul 12 2013

PARI

Vec(1/((1-x)*(1-x^2)^2*(1-x^3)^3*(1-x^4)^4)+O(x^66)) \\ Joerg Arndt, Jul 11 2013