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Search: id:A024490
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| A024490 |
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a(n) = C(n-1,1) + C(n-3,3) + ... + C(n-2m-1,2m+1), where m = floor((n-2)/4). |
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+0
7
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| 1, 2, 3, 4, 6, 10, 17, 28, 45, 72, 116, 188, 305, 494, 799, 1292, 2090, 3382, 5473, 8856, 14329, 23184, 37512, 60696, 98209, 158906, 257115, 416020, 673134, 1089154, 1762289, 2851444, 4613733, 7465176, 12078908, 19544084, 31622993, 51167078, 82790071
(list; graph; listen)
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OFFSET
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2,2
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COMMENT
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Essentially both the first difference sequence and partial sum of A005252, so its own shifted second difference, and indeed virtually the same as A005252, so close to being its own shifted first difference.
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LINKS
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T. D. Noe, Table of n, a(n) for n=2..502
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 886
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FORMULA
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2a(n)=F(n+1)-A010892(n), F(n) = n-th Fibonacci number. - Mario Catalani (mario.catalani(AT)unito.it), Jan 08 2003
a(n)=sum{k=0..n, Fib(k+1)2sin(pi(n-k)/3+pi/3)/sqrt(3) } - Paul Barry (pbarry(AT)wit.ie), May 18 2004
G.f.: -1/((x^2+x-1)(x^2-x+1)) - Jon Perry (perry(AT)globalnet.co.uk), Jun 22 2004
a(n)=sum{k=0..floor(n/2), C(n-k+1,k+1)*(1+(-1)^k)/2}; - Paul Barry (pbarry(AT)wit.ie), Jul 05 2007
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CROSSREFS
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a(n)=A000045(n+1)-A005252(n).
Cf. A010892.
Sequence in context: A026502 A060163 A106511 this_sequence A056469 A004047 A093912
Adjacent sequences: A024487 A024488 A024489 this_sequence A024491 A024492 A024493
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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Additional comments from Henry Bottomley (se16(AT)btinternet.com), Apr 07 2000
Corrected by Mario Catalani (mario.catalani(AT)unito.it), Jan 08 2003
Further corrections from Hugo van der Sanden (hv(AT)crypt.org), Oct 05 2006
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