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A006367
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Number of binary vectors beginning with 0 and containing just 1 singleton.
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2
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1, 0, 2, 2, 5, 8, 15, 26, 46, 80, 139, 240, 413, 708, 1210, 2062, 3505, 5944, 10059, 16990, 28646, 48220, 81047, 136032, 228025, 381768, 638450, 1066586, 1780061, 2968040, 4944519, 8230370, 13689118, 22751528, 37786915, 62716752, 104028245
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Number of compositions of n+1 containing exactly one 1. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 08 2002
Number of permutations with one fixed point avoiding 231 and 321.
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LINKS
| T. Mansour and A. Robertson, Refined restricted permutations....
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FORMULA
| a(n)=a(n-1)+a(n-2)+Fibonacci(n-3).
G.f.: (1-x)^2/(1-x-x^2)^2 - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 08 2002
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EXAMPLE
| a(4)=5 because among the 2^4 compositions of 5 only 4+1,1+4,2+2+1,2+1+2,1+2+2 contain exactly one 1.
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CROSSREFS
| Sequence in context: A056224 A052527 A042982 * A077902 A005834 A052531
Adjacent sequences: A006364 A006365 A006366 * A006368 A006369 A006370
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KEYWORD
| nonn,easy
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AUTHOR
| David M. Bloom.
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EXTENSIONS
| More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
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