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Search: id:A059841
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| A059841 |
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A simple periodic sequence. |
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+0
54
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| 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0
(list; table; graph; listen)
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OFFSET
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0,1
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COMMENT
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When viewed as an array the row sum values are 1 1 1 2 3 3 3 4 5 5 5 6 ... A004525
This is the r=0 member of the r-family of sequences S_r(n) defined in A092184 where more information can be found.
Successive binomial transforms of this sequence : A011782, A007051, A007582, A081186, A081187, A081188, A081189, A081190, A060531, A081192
Characteristic function of even numbers: a(A005843(n))=1, a(A005408(n))=0. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 29 2008]
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REFERENCES
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Paul Barry, A Catalan Transform and Related Transformations on Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5.
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LINKS
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Index entries for sequences related to linear recurrences with constant coefficients
Index entries for characteristic functions
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FORMULA
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G.f.: 1/(1-x^2). E.g.f.: cosh(x). a(n)=(n+1)mod 2. a(n)=1/2 + (-1)^n/2. - Paul Barry (pbarry(AT)wit.ie), Mar 11 2003
T(n, k)=([n/2]+n+k+1)mod 2, 0<=k<=n.
Additive with a(p^e) = 1 if p = 2, 0 otherwise.
a(n)= {sin[(n+1)*Pi/2]}^2 = [cos(n*Pi/2)]^2 with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Nov 17 2006
a(n)= Sum_{k, 0<=k<=n}(-1)^k*A038137(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 30 2006
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MAPLE
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with(combstruct):ZL2:=[S, {S=Set(Cycle(Z, card=2))}, unlabeled]:seq(count(ZL2, size=n), n=0..100); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 24 2007
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MATHEMATICA
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CellularAutomaton[50, {{1}, 0}, 104, {All, {0}}] // Flatten [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 08 2009]
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PROGRAM
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(PARI) {a(n)=(n+1)%2} {T(n, k)=if(k<0|k>n, 0, (n\2+n+k+1)%2)}
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CROSSREFS
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Ones complement of A000035. Cf. A004525, A011782.
Sequence in context: A101455 A056594 A091337 this_sequence A071022 A071025 A162549
Adjacent sequences: A059838 A059839 A059840 this_sequence A059842 A059843 A059844
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Alford Arnold (Alford1940(AT)aol.com), Feb 25 2001
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