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Search: id:A032766
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| A032766 |
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Congruent to 0 or 1 mod 3. |
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+0
23
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| 0, 1, 3, 4, 6, 7, 9, 10, 12, 13, 15, 16, 18, 19, 21, 22, 24, 25, 27, 28, 30, 31, 33, 34, 36, 37, 39, 40, 42, 43, 45, 46, 48, 49, 51, 52, 54, 55, 57, 58, 60, 61, 63, 64, 66, 67, 69, 70, 72, 73, 75, 76, 78, 79, 81, 82, 84, 85, 87, 88, 90, 91, 93, 94, 96, 97, 99, 100, 102, 103
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Also (omitting initial 0) number of 1's in n-th row of triangle in A071039. - Hans Havermann (pxp(AT)rogers.com), May 26 2002
Binomial transform is A053220. - Michael Somos, Jul 10 2003
Smallest number of different people in a set of n-1 photographs which satisfies the following conditions: In each photograph there are 3 women, the woman in the middle is the mother of the person on her left and is a sister of the person on her right and the women in the middle of the photographs are all different. - Fung Cheok Yin (cheokyin_restart(AT)yahoo.com.hk), Sep 22 2006
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REFERENCES
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International Mathematical Olympiad 2001, Hong Kong Preliminary Selection Contest Problem #20.
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FORMULA
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G.f.: (x+2*x^2)/((1-x)*(1-x^2)).
Formulae from Paul Barry (pbarry(AT)wit.ie), Sep 04 2003: a(n)=(6*n-1+(-1)^n)/4; a(n)=floor((3n+2)/2)-1 = A001651(n)-1; a(n)=sqrt(2)*sqrt((6n-1)(-1)^n+18n^2-6n+1)/4; a(n)=sum{k=0..n, 3/2-2*0^n+(-1)^n/2}.
a(n) = 3*floor(n/2) + n mod 2 = A007494(n)-A000035(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Apr 04 2005
a(n)=2*A004526(n)+A004526(n+1). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 07 2006
a(n) = 1 + ceiling(1.5*(n-1)) - Fung Cheok Yin (cheokyin_restart(AT)yahoo.com.hk), Sep 22 2006
Row sums of triangle A133083. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 08 2007
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MAPLE
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a[0]:=0:a[1]:=1:for n from 2 to 100 do a[n]:=a[n-2]+3 od: seq(a[n], n=0..69); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 16 2008
seq(add(irem(2^k, 3), k=2..n), n=1..70); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 20 2008
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PROGRAM
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(PARI) a(n)=n+n\2.
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CROSSREFS
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For n>0, a(n)=T(n, 2), array T as in A049615. Column 1 of A026374.
Partial sums are A006578. Partial sums of A000034. Cf. A084056, A047270.
Cf. A001651, A007494, A035360, A132463.
Cf. A133083.
Sequence in context: A026322 A049624 A084056 this_sequence A064717 A109231 A140098
Adjacent sequences: A032763 A032764 A032765 this_sequence A032767 A032768 A032769
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Patrick De Geest (pdg(AT)worldofnumbers.com), May 15, 1998.
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EXTENSIONS
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Better description from njas 8/98.
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