A025829 Expansion of 1/((1-x^3)*(1-x^4)*(1-x^7)).
1, 0, 0, 1, 1, 0, 1, 2, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 7, 8, 9, 9, 9, 10, 11, 11, 11, 12, 13, 13, 13, 15, 15, 15, 16, 17, 17, 18, 19, 19, 20, 21, 21, 22, 23, 24, 24, 25, 26, 27, 27, 28, 30, 30, 30
Offset: 0
Examples
There are 7 partitions of 27 into parts 3,4 and 7. These are (77733)(774333)(744444)(7443333)(4444443)(44433333)(333333333). - _David Neil McGrath_, Sep 08 2014
Links
- Robert Israel, Table of n, a(n) for n = 0..10000
- F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, A slow-growing sequence defined by an unusual recurrence, J. Integer Sequences, Vol. 10 (2007), #07.1.2.
- Index entries for sequences related to Gijswijt's sequence
- Index entries for linear recurrences with constant coefficients, signature (0,0,1,1,0,0,0,0,0,-1,-1,0,0,1).
Programs
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Maple
f:= gfun:-rectoproc({a(0) = 1, a(1) = 0, a(2) = 0, a(3) = 1, a(4) = 1, a(5) = 0, a(6) = 1, a(7) = 2, a(8) = 1, a(9) = 1, a(10) = 2, a(11) = 2, a(12) = 2, a(13) = 2, a(n) = a(n-3)+a(n-4)-a(n-10)-a(n-11)+a(n-14)},a(n),'remember'): seq(f(n),n=0..100); # Robert Israel, Sep 08 2014 -
Mathematica
LinearRecurrence[{0,0,1,1,0,0,0,0,0,-1,-1,0,0,1}, {1,0,0,1,1,0,1,2,1,1,2,2,2,2}, 80] (* Jean-François Alcover, Aug 21 2022 *) -
PARI
a(n)=floor((-2)^(n%3\2)/9-(n%2)*(-1)^(n\2)/4+(3*n^2+42*n+448)/504) \\ Tani Akinari, Aug 19 2013
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PARI
Vec(1/((1-x^3)*(1-x^4)*(1-x^7)) + O(x^80)) \\ Michel Marcus, Sep 08 2014
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PARI
a(n) = (n^2 +14*n -56*[0,0,1][n%3+1] +21*[8,5,8,9][n%4+1])\168 \\ Hoang Xuan Thanh, Sep 01 2025
Formula
a(n) = a(n-3)+a(n-4)-a(n-10)-a(n-11)+a(n-14). - David Neil McGrath, Sep 08 2014
a(n) = floor(((n+1)*(n+13) + 19*(((n+1) mod 3) - (n mod3)))/168 + ((n mod 4)-1)*(3*(n mod 4)-5)/8 + ((n+1) mod 4)/4). - Hoang Xuan Thanh, Sep 01 2025
Comments