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Search: id:A072951
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| A072951 |
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a(n)=sum(k>=2,z(k)*v(k)^n) where v(k) is the real positive solution to x^k=x+1 (i.e. the k-th Pisot-Vijayaraghavan number) and z(k) is the real positive root of a polynomial P(k,x) with integer coefficients of degree k. |
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+0
1
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| 1, 2, 4, 6, 11, 15, 27, 39, 63, 100, 159, 247, 403, 641, 1023, 1644, 2653, 4264, 6872, 11081, 17895, 28899, 46680, 75420, 121918, 197113, 318728, 515420, 833592, 1348309, 2181022, 3528144, 5707568, 9233629, 14938481, 24168531, 39102324
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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In particular a(n) is asymptotic to (1/10)*(5+sqrt(5))*phi^n where phi is the golden ratio. First P(k,x) are P(2,x)=5x^2-5x-1; P(3,x)=23x^3-23x^2+8x-1; P(4)=283x^4-283x^3+105x^2-17x+1; P(5)=2869x^5-2869x^4+1154x^3-234x^2+24x -1
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FORMULA
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a(n)=sum(k=1, n, C(k, n modk)) - Benoit Cloitre (benoit7848c(AT)orange.fr), May 03 2003
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PROGRAM
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(PARI) a(n)=sum(k=1, n, binomial(k, n%k))
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CROSSREFS
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Sequence in context: A138461 A103580 A094866 this_sequence A062766 A115269 A103692
Adjacent sequences: A072948 A072949 A072950 this_sequence A072952 A072953 A072954
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 20 2002
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