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Search: id:A003440
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| A003440 |
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Number of binary vectors with restricted repetitions.
(Formerly M2666)
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+0
3
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| 1, 1, 3, 7, 17, 42, 104, 259, 648, 1627, 4098, 10350, 26202, 66471, 168939, 430071, 1096451, 2799072, 7154189, 18305485, 46885179, 120195301, 308393558, 791882862
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The sum of squared terms in row n of A104402 = 2*a(n) for n>0. - Paul D. Hanna (pauldhanna(AT)juno.com), Mar 06 2005
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
K. A. Post, Binary Sequences with Restricted Repetitions. Report 74-WSK-02, Math. Dept., Tech. Univ. Eindhoven, May. 1974.
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FORMULA
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G.f.: {(1-x)^2 * sqrt[(1+x+x^2)/(1-3x+x^2)] + x^2 - 1}/(2x^2) (conjectured). - R. Stephan, Mar 28 2004
a(n) = Sum_{k=0..n} (C(k, n-k) + C(k+1, n-k-1))^2 for n>0, with a(0)=1. - Paul D. Hanna (pauldhanna(AT)juno.com), Mar 06 2005
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PROGRAM
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(PARI) {a(n)=polcoeff(((1-x)^2*sqrt((1+x+x^2)/(1-3*x+x^2))+x^2-1)/(2*x^2)+x*O(x^n), n)} (PARI) {a(n)=if(n==0, 1, sum(k=0, n, (binomial(k, n-k)+binomial(k+1, n-k-1))^2)/2)} (Hanna)
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CROSSREFS
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Cf. A078678.
Cf. A104402.
Sequence in context: A058351 A086395 A020730 this_sequence A102071 A161943 A134184
Adjacent sequences: A003437 A003438 A003439 this_sequence A003441 A003442 A003443
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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