|
Search: id:A035959
|
|
|
| A035959 |
|
Number of partitions of n in which no parts are multiples of 5. |
|
+0
12
|
|
| 1, 1, 2, 3, 5, 6, 10, 13, 19, 25, 34, 44, 60, 76, 100, 127, 164, 205, 262, 325, 409, 505, 628, 769, 950, 1156, 1414, 1713, 2081, 2505, 3026, 3625, 4352, 5192, 6200, 7364, 8756, 10357, 12258, 14450, 17034, 20006, 23500, 27510, 32200, 37582, 43846, 51022
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
Also number of partitions with at most 4 parts of size 1 and differences between parts at distance 6 are greater than 1.
Also number of partitions of n where no part appears more than four times.
Case k=7,i=5 of Gordon Theorem.
|
|
REFERENCES
|
G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=0..1000
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
|
|
FORMULA
|
G.f.: product(j=1, oo, 1 + x^j + x^2j + x^3j + x^4j) - Jon Perry (perry(AT)globalnet.co.uk), Mar 30 2004
G.f.: prod[n>0, n==1, 2, 3, 4 mod 5, 1/(1-q^n) ].
Given g.f. A(x) then B(x)=x*A(x^3)^2 satisfies 0=f(B(x), B(x^2)) where f(u,v)= u^3 +v^3 -u*v -5*u^2*v^2 . - Michael Somos May 28 2006
Given g.f. A(x) then B(x)=x*A(x^3)^2 satisfies 0=f(B(x), B(x^2), B(x^4)) where f(u,v,w)= +v +5*v^2*(u+w) -(u^2+u*w+w^2) . - Michael Somos May 28 2006
Euler transform of period 5 sequence [ 1, 1, 1, 1, 0, ...]. - Michael Somos May 28 2006
G.f. is product k>0 P5(x^k) where P5 is 5th cyclotomic polynomial.
|
|
PROGRAM
|
(PARI) {a(n)=if(n<0, 0, polcoeff( eta(x^5+x*O(x^n))/ eta(x+x*O(x^n)), n))} /* Michael Somos May 28 2006 */
|
|
CROSSREFS
|
Cf. A000726, A001935, A000009, A061198, A061199.
Adjacent sequences: A035956 A035957 A035958 this_sequence A035960 A035961 A035962
Sequence in context: A018429 A035953 A087750 this_sequence A036801 A035966 A035974
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
Olivier Gerard (olivier.gerard(AT)gmail.com)
|
|
|
Search completed in 0.003 seconds
|
