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Search: id:A107903
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| A107903 |
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Generalized NSW numbers. |
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+0
3
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| 1, 10, 76, 568, 4240, 31648, 236224, 1763200, 13160704, 98232832, 733219840, 5472827392, 40849739776, 304906608640, 2275853910016, 16987204845568, 126794223124480, 946404965613568, 7064062832410624, 52726882796830720
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Counts total area under elevated Schroeder paths of length 2n+2, where where horizontal steps can choose from three colors.
Case r=4 for family (1+(r-1)x)/(1-2(1+r)x+(1-r)^2*x^2). Case r=2 gives NSW numbers A002315.
Fifth binomial transform of (1+8x)/(1-16x^2), A107906.
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FORMULA
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G.f.: (1+2x)/(1-8x+x^2); a(n)=sum{k=0..n, binomial(2n+1, 2k)3^k}; a(n)=((1+sqrt(3))(4+2sqrt(3))^n+(1-sqrt(3))(4-2sqrt(3))^n)/2.
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CROSSREFS
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Sequence in context: A061319 A016149 A081199 this_sequence A075489 A000808 A140763
Adjacent sequences: A107900 A107901 A107902 this_sequence A107904 A107905 A107906
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 27 2005
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