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A004524
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Three even followed by one odd.
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15
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0, 0, 0, 1, 2, 2, 2, 3, 4, 4, 4, 5, 6, 6, 6, 7, 8, 8, 8, 9, 10, 10, 10, 11, 12, 12, 12, 13, 14, 14, 14, 15, 16, 16, 16, 17, 18, 18, 18, 19, 20, 20, 20, 21, 22, 22, 22, 23, 24, 24, 24, 25, 26, 26, 26, 27, 28, 28, 28, 29, 30, 30, 30, 31, 32, 32, 32, 33, 34, 34, 34, 35, 36, 36, 36, 37
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| a(n) = A092038(n-3) for n>4. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 28 2004
Ignoring the first term, for n>=0, n/2 rounded by the method called "banker's rounding", "statistician's rounding", or "round-to-even" gives 0,0,1,2,2,2,3,..., where this method rounds k+.5 to k if positive integer k is even but rounds k+.5 to k+1 when k+1 is even. (If the method is indeed defined such that the above statement is also true with the word "positive" removed, then the first 0 term need not be ignored and this sequence can be further extended symmetrically with a(m) = -a(-m) for all integers m, an advantage over usual rounding). The corresponding sequence for n/2 rounded by the common method is A004526 (considered as beginning with n=-1). - Rick L. Shepherd (rshepherd2(AT)hotmail.com), Nov 16 2006
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Index entries for two-way infinite sequences
Wikipedia, Rounding
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FORMULA
| a(n) = a(n-1)-a(n-2)+a(n-3)+1 = (n-1)-A004525(n-1) - Henry Bottomley (se16(AT)btinternet.com), Mar 08 2000
G.f.: x^3/((1-x)^2(1+x^2))=x^3(1-x^2)/((1-x)^2(1-x^4)). a(n)=-a(2-n).
E.g.f. : exp(x)(x-1)/2+cos(x)/2; a(n)=(n-2)/2+1/2-cos(pi*(n-2)/2)/2. - Paul Barry (pbarry(AT)wit.ie), Oct 27 2004
a(n+3)=sum{k=0..n, (1+(-1)^C(n,2))/2}; - Paul Barry (pbarry(AT)wit.ie), Mar 31 2008
a(n)=(1/2)*(n-1)+(1/4)*[I^n+(-I)^n], with n>=0 and I=sqrt(-1) [From Paolo P. Lava (paoloplava(AT)gmail.com), Dec 16 2008]
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MATHEMATICA
| s=0; w1=0; w2=0; lst={w1, w2}; Do[s+=n-w1-w2; AppendTo[lst, s]; w1=w2; w2=s, {n, 0, 2*5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 26 2008]
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PROG
| (PARI) a(n)=n\4+(n+1)\4
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CROSSREFS
| Cf. A004525.
Zero followed by partial sums of A021913.
Cf. A093390, A093393, A093391, A093392.
First differences of A011848.
Sequence in context: A113512 A194169 A194165 * A126257 A025773 A029077
Adjacent sequences: A004521 A004522 A004523 * A004525 A004526 A004527
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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