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Search: id:A062318
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| A062318 |
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Numbers n such that no entry in n-th row of Pascal's triangle is divisible by 3, i.e. such that A062296(n) = 0. |
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9
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| 0, 1, 2, 5, 8, 17, 26, 53, 80, 161, 242, 485, 728, 1457, 2186, 4373, 6560, 13121, 19682, 39365, 59048, 118097, 177146, 354293, 531440, 1062881, 1594322, 3188645, 4782968, 9565937, 14348906, 28697813, 43046720, 86093441, 129140162
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OFFSET
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1,3
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COMMENT
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The base 3 representation of these numbers is 222...222 or 122...222.
Smallest number with ternary digit sum = n: A053735(a(n)) = n and A053735(m) <> n for m < a(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 15 2006
A138002(a(n)) = 0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 26 2008
The initial terms suggest that this sequence is the same as A112346. Is that a coincidence or a theorem? - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 07 2008
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REFERENCES
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Gy. Tasi and F. Mizukami, Quantum algebraic-combinatoric study of the conformational properties of n-alkanes, J. Math. Chemistry, 25, 1999, 55-64 (see p. 60).
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FORMULA
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These are the numbers of the form 3^m - 1 or 2*3^m - 1 i.e. the union of sequences A048473 and A024023.
a(n)=3^(n/2)-1 if n is even; a(n)=2*3^(n/2-1/2)-1 if n is odd. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 03 2005
a(n)=a(n-1)+3a(n-2)-3a(n-3). Differences: A108411. - Paul Curtz (bpcrtz(AT)free.fr), Feb 21 2008
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EXAMPLE
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The first rows in Pascal's triangle with no multiples of 3 are:
row 0: 1;
row 1: 1,1;
row 2: 1,2,1;
row 5: 1,5,10,10,5,1;
row 8: 1,8,28,56,70,56,28,8,1;
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MAPLE
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a:=proc(n) if n mod 2 = 0 then 3^(n/2)-1 else 2*3^((n-1)/2)-1 fi end: seq(a(n), n=0..37); (Deutsch)
a[0]:=0:a[1]:=1:for n from 2 to 100 do a[n]:=3*a[n-2]+2 od: seq(a[n], n=0..34); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 17 2008
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CROSSREFS
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Cf. A062296, A024023, A048473.
Sequence in context: A055236 A103041 A006827 this_sequence A112346 A034445 A054754
Adjacent sequences: A062315 A062316 A062317 this_sequence A062319 A062320 A062321
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KEYWORD
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nonn
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AUTHOR
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Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 05 2001
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 03 2005
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