A029033 Expansion of 1/((1-x)(1-x^3)(1-x^4)(1-x^7)).

1, 1, 1, 2, 3, 3, 4, 6, 7, 8, 10, 12, 14, 16, 19, 22, 25, 28, 32, 36, 40, 45, 50, 55, 61, 67, 73, 80, 88, 95, 103, 112, 121, 130, 140, 151, 162, 173, 185, 198, 211, 224, 239, 254, 269, 285, 302, 319, 337, 356, 375, 395

Offset

0,4

Comments

Number of partitions of n into parts 1, 3, 4 and 7. - Ilya Gutkovskiy, May 14 2017

Links

Table of n, a(n) for n=0..51.

Index entries for linear recurrences with constant coefficients, signature (1, 0, 1, 0, -1, 0, 0, 0, 0, -1, 0, 1, 0, 1, -1).

Formula

a(0)=1, a(1)=1, a(2)=1, a(3)=2, a(4)=3, a(5)=3, a(6)=4, a(7)=6, a(8)=7, a(9)=8, a(10)=10, a(11)=12, a(12)=14, a(13)=16, a(14)=19, a(n) = a(n-1) + a(n-3) - a(n-5) - a(n-10) + a(n-12) + a(n-14) - a(n-15). - Harvey P. Dale, Feb 26 2012

Maple

M := Matrix(15, (i, j)-> if (i=j-1) or (j=1 and member(i, [1, 3, 12, 14])) then 1 elif j=1 and member(i, [5, 10, 15]) then -1 else 0 fi); a := n -> (M^(n))[1, 1]; seq (a(n), n=0..51); # Alois P. Heinz, Jul 25 2008

Mathematica

CoefficientList[Series[1/((1-x)(1-x^3)(1-x^4)(1-x^7)), {x, 0, 60}], x] (* or *) LinearRecurrence[{1, 0, 1, 0, -1, 0, 0, 0, 0, -1, 0, 1, 0, 1, -1}, {1, 1, 1, 2, 3, 3, 4, 6, 7, 8, 10, 12, 14, 16, 19}, 60] (* Harvey P. Dale, Feb 26 2012 *)

Crossrefs

Sequence in context: A256211 A265109 A301277 * A041003 A067592 A101195

Adjacent sequences: A029030 A029031 A029032 * A029034 A029035 A029036

Keyword

nonn

Author

N. J. A. Sloane

Status

approved