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Search: id:A061551
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| A061551 |
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Number of paths along a corridor width 8, starting from one side. |
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+0
3
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| 1, 1, 2, 3, 6, 10, 20, 35, 69, 124, 241, 440, 846, 1560, 2977, 5525, 10490, 19551, 36994, 69142, 130532, 244419, 460737, 863788, 1626629, 3052100, 5743674, 10782928, 20283121, 38092457, 71632290, 134560491, 252989326, 475313762
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Counts all paths of length n starting at initial node on the path graph P_8. - Paul Barry (pbarry(AT)wit.ie), May 11 2004
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FORMULA
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a(n)=sum(b(n, i)) where b(n, 0)=b(n, 9)=0, b(0, 1)=1, b(0, n)=0 if n!=1 and b(n, i)=b(n-1, i)+b(n+1, i) if 0<n<9.
G.f.=(1-2x^2)/[(1-x)(1-3x^2-x^3)]. a(n)=7a(n-2)-15a(n-4)+10a(n-6)-a(n-8). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 14 2006
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MAPLE
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a[0]:=1: a[1]:=1: a[2]:=2: a[3]:=3: a[4]:=6: a[5]:=10: a[6]:=20: a[7]:=35: for n from 8 to 33 do a[n]:=7*a[n-2]-15*a[n-4]+10*a[n-6]-a[n-8] od: seq(a[n], n=0..33); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 14 2006
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CROSSREFS
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Narrower corridors effectively produce A000007, A000012, A016116, A000045, A038754, A028495, A030436. An infinitely wide corridor (i.e. just one wall) would produce A001405.
a(n) = A094718(8, n).
Adjacent sequences: A061548 A061549 A061550 this_sequence A061552 A061553 A061554
Sequence in context: A077027 A030436 A030227 this_sequence A026034 A037031 A056202
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), May 16 2001
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