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Search: id:A089508
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| A089508 |
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Solution to a binomial problem together with companion sequence A081016(n-1). |
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+0
4
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| 1, 14, 103, 713, 4894, 33551, 229969, 1576238, 10803703, 74049689, 507544126, 3478759199, 23843770273, 163427632718, 1120149658759, 7677619978601, 52623190191454, 360684711361583, 2472169789339633, 16944503814015854
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) and b(n) := A081016(n-1) are the solutions to the Diophantine equation binomial(a,b)=binomial(a+1,b-1). The first few binomials are given by A090162(n).
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REFERENCES
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A. I. Shirshov: On the equation binomial(n,m)=binomial(n+1,m-1), pp. 83-86, in: Kvant Selecta: Algebra and Analysis, I, ed. S. Tabachnikov, Am.Math.Soc., 1999
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FORMULA
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G.f.: x*(1+6*x-x^2)/((1-x)*(1-7*x+x^2)).
a(n)=A081018(n)-1 = F(2*n)*F(2*n+1)-1, n>=1; with F(n) := A000045(n) (Fibonacci).
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EXAMPLE
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n = 2: a(2) = 14, b(2) = A081016(1) = 6 satisfy binomial(14,6) = 3003 = binomial(15,5). 3003 = A090162(2).
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CROSSREFS
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Equals A081018 - 1.
Sequence in context: A041370 A055913 A005757 this_sequence A131709 A139614 A068390
Adjacent sequences: A089505 A089506 A089507 this_sequence A089509 A089510 A089511
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Dec 01 2003
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