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A024490
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a(n) = C(n-1,1) + C(n-3,3) + ... + C(n-2*m-1,2*m+1), where m = floor((n-2)/4).
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9
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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; refs; listen; history; internal format)
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OFFSET
| 2,2
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COMMENTS
| 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.
From Paul Curtz, Jun 22 2011. (Start)
b(n)=0,0,0,1,2,3,4,6, and differences are
0, 0, 0, 1, 2, 3, 4, 6,
0, 0, 1, 1, 1, 1, 2, 4,
0, 1, 0, 0, 0, 1, 2, 3,
1, -1, 0, 0, 1 , 1, 1, 1,
-2, 1, 0, 1, O, 0, 0, 1,
3, -1, 1 -1, 0, 0, 1, 1,
-4, 2, -2, 1, 0, 1, 0, 0,
6, -4, 3, -1, 1, -1, 0, 0;
b(n) is an eigensequence (sequence identical to its inverse binomial transform signed) of first kind i.e. its main diagonal is A000004.
Examples:A000045, A001045, A113405, A191754 (array). (End)
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LINKS
| T. D. Noe, Table of n, a(n) for n=2..502
Fumio Hazama, Spectra of graphs attached to the space of melodies, Discr. Math., 311 (2011), 2368-2383. See Table 2.1.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 886
Index to sequences with linear recurrences with constant coefficients, signature (2,-1,0,1).
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FORMULA
| a(n)=A000045(n+1)-A005252(n).
2*a(n)=A000045(n+1)-A010892(n). - Mario Catalani (mario.catalani(AT)unito.it), Jan 08 2003
a(n)=sum{k=0..n, Fib(k+1)*2*sin(pi*(n-k)/3+pi/3)/sqrt(3) } - Paul Barry (pbarry(AT)wit.ie), May 18 2004
G.f.: -x^2/((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
| Cf. A010892.
Sequence in context: A026502 A060163 A106511 * A056469 A004047 A093912
Adjacent sequences: A024487 A024488 A024489 * A024491 A024492 A024493
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KEYWORD
| nonn,easy
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| 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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