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A025876 Expansion of 1/((1-x^5)(1-x^6)(1-x^7)). 0
1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 7, 6, 6, 7, 7, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 10, 11, 12, 12, 12, 12, 12, 13, 14, 14, 14, 14, 15, 15 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,13

COMMENTS

With a(0)=0, a(n) is the number of partitions of n into 4 parts whose largest part is twice the smallest part. - Wesley Ivan Hurt, Jan 06 2021

a(n) is the number of partitions of n into parts 5, 6, and 7. - Joerg Arndt, Jan 06 2021

LINKS

Table of n, a(n) for n=0..71.

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

FORMULA

a(n) = a(n-5)+a(n-6)+a(n-7)-a(n-11)-a(n-12)-a(n-13)+a(n-18). - Harvey P. Dale, Dec 16 2013

For n > 0, a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} [3*k = n-i-j], where [ ] is the Iverson bracket. - Wesley Ivan Hurt, Jan 06 2021

MATHEMATICA

CoefficientList[Series[1/((1-x^5)(1-x^6)(1-x^7)), {x, 0, 80}], x] (* or *) LinearRecurrence[{0, 0, 0, 0, 1, 1, 1, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 2, 1, 1, 1, 1, 2}, 80] (* Harvey P. Dale, Dec 16 2013 *)

CROSSREFS

Sequence in context: A328523 A025887 A025882 * A109035 A244231 A237706

Adjacent sequences:  A025873 A025874 A025875 * A025877 A025878 A025879

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 25 06:19 EST 2022. Contains 350565 sequences. (Running on oeis4.)