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A035985
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Number of partitions of n into parts not of the form 21k, 21k+7 or 21k-7. Also number of partitions with at most 6 parts of size 1 and differences between parts at distance 9 are greater than 1.
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1
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1, 1, 2, 3, 5, 7, 11, 14, 21, 28, 39, 51, 70, 90, 119, 153, 199, 252, 324, 406, 515, 642, 804, 994, 1236, 1517, 1869, 2282, 2791, 3387, 4118, 4970, 6006, 7217, 8673, 10374, 12411, 14780, 17601, 20883, 24766, 29274, 34588, 40741, 47964, 56319, 66080
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Case k=10,i=7 of Gordon Theorem.
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REFERENCES
| G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
Watson, G. N.; Ramanujans Vermutung ueber Zerfaellungsanzahlen. J. Reine Angew. Math. (Crelle), 179 (1938), 97-128. This sequence arises as the coefficients of Y = C/B on p. 118. [Added by N. J. A. Sloane, Nov 13 2009]
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LINKS
| GDZ, Digitized volumes of Crelle [Added by N. J. A. Sloane, Nov 13 2009]
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FORMULA
| Euler transform of period 7 sequence [1, 1, 1, 1, 1, 1, 0, ...]. - Michael Somos Jan 17 2006
Given g.f. A(x), then B(x)=x*A(x^4) satisfies 0=f(B(x), B(x^3)) where f(u, v)=(u^4+v^4)-u*v*(1+3*u*v+7*(u*v)^2).
G.f.: Product_{k>0} (1-x^(7k))/(1-x^k).
Given g.f. A(x) then B(x)=x*A(x)^4 satisfies 0=f(B(x), B(x^2), B(x^4)) where f(u,v,w)= (u^2+u*w+w^2) -v -8*v*(u+v+w) -49*v^2*(u+w) . - Michael Somos May 28 200
G.f. is product k>0 P7(x^k) where P7 is 7th cyclotomic polynomial.
Expansion of q^(-1/4)eta(q^7)/eta(q) in powers of q. - Michael Somos Jan 17 2006
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EXAMPLE
| B(x) = x +x^5 +2*x^9 +3*x^13 +5*x^17 +7*x^21 +11*x^25 +14*x^29 +...
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PROG
| (PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^7+A)/eta(x+A), n))} /* Michael Somos Jan 17 2006 */
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CROSSREFS
| Sequence in context: A035968 A112581 A035976 * A035995 A036006 A027341
Adjacent sequences: A035982 A035983 A035984 * A035986 A035987 A035988
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KEYWORD
| nonn,easy
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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