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Search: id:A137821
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| A137821 |
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Numbers n such that sum( Catalan(k), k=1..2n) = 0 (mod 3). |
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+0
7
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| 1, 4, 6, 13, 15, 18, 19, 40, 42, 45, 46, 54, 55, 58, 60, 121, 123, 126, 127, 135, 136, 139, 141, 162, 163, 166, 168, 175, 177, 180, 181, 364, 366, 369, 370, 378, 379, 382, 384, 405, 406, 409, 411, 418, 420, 423, 424, 486, 487, 490, 492, 499, 501, 504, 505
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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It would be natural to pre-pend an initial term a(1)=0 (for which the sum is to be considered empty, thus zero), but we omit it to avoid confusion w.r.t. indices of A107755.
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LINKS
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M. F. Hasler, Table of n, a(n) for n=1,...,499.
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FORMULA
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a(n) = A107755(n)/2 = sum( A137822(k), k=0..n)
a(2^j) = 2 a(2^j-1) + 1 (resp. +2) for j even (resp. odd).
sum( Catalan(k), k=1..2n) = sum( Catalan(2k-1) * (10k-1)/(2k+1), k=1..n), thus:
{ a(m) } = { n>0 | sum( Catalan(2k-1) * (10k-1)/(2k+1), k=1..n) = 0 (mod 3) }.
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PROGRAM
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(PARI) n=0; A137821=vector(499, i, { if( bitand(i, i-1), while(n++ & s+=binomial(4*n-2, 2*n-1)/(2*n)*(10*n-1)/(2*n+1), ), s=Mod(0, 3); n=2*n+1+log(i+.5)\log(2)%2 ); n})
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CROSSREFS
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Cf. A107755 (twice this), A137822-A137824.
Sequence in context: A003973 A034747 A074165 this_sequence A010061 A063186 A069061
Adjacent sequences: A137818 A137819 A137820 this_sequence A137822 A137823 A137824
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KEYWORD
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nonn
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AUTHOR
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M. F. Hasler (MHasler(AT)univ-ag.fr), Feb 25 2008
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