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Search: id:A003116
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| A003116 |
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Expansion of reciprocal of a determinant.
(Formerly M1068)
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+0
8
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| 1, 1, 2, 4, 7, 13, 23, 41, 72, 127, 222, 388, 677, 1179, 2052, 3569, 6203, 10778, 18722, 32513, 56455, 98017, 170161, 295389, 512755, 890043, 1544907, 2681554, 4654417, 8078679, 14022089, 24337897, 42242732, 73319574, 127258596, 220878683
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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G.f. is reciprocal of g.f. of A039924.
Conjecture: a(n) is the number of compositions (a_1,a_2,...) of n with each a_i-a_(i-1) <= 1; cf. A034297. - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 09 2004
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REFERENCES
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D. H. Lehmer, Lecture course on history of mathematics, Univ. Calif. Berkeley, 1973.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..400
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FORMULA
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G.f.: 1/(Sum_{k>=0} x^(k^2)(-1)^k/(Product_{i=1..k} 1-x^i)).
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EXAMPLE
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1+x^2+2*x^4+4*x^6+7*x^8+13*x^10+23*x^12+...
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PROGRAM
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(PARI) a(n)=if(n<0, 0, polcoeff(1/sum(k=0, sqrtint(n), x^k^2/prod(i=1, k, x^i-1, 1+x*O(x^n))), n))
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CROSSREFS
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Cf. A003114, A039924.
Cf. A034297.
Sequence in context: A128609 A114832 A136299 this_sequence A165648 A078038 A048888
Adjacent sequences: A003113 A003114 A003115 this_sequence A003117 A003118 A003119
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Herman P. Robinson
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