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Search: id:A025581
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| A025581 |
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Triangle T(n,k) = n-k, n >= 0, 0<=k<=k. Integers m to 0 followed by integers m+1 to 0 etc. |
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+0
51
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| 0, 1, 0, 2, 1, 0, 3, 2, 1, 0, 4, 3, 2, 1, 0, 5, 4, 3, 2, 1, 0, 6, 5, 4, 3, 2, 1, 0, 7, 6, 5, 4, 3, 2, 1, 0, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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The PARI functions t1, t2 can be used to read a square array T(n,k) (n >= 0, k >= 0) by antidiagonals upwards: n -> T(t1(n), t2(n)). - Michael Somos, Aug 23, 2002
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LINKS
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M. Somos, Sequences used for indexing triangular or square arrays
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FORMULA
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a(n) = (((trinv(n)-1)*(((1/2)*trinv(n))+1))-n) # Cf. A002262
G.f.: y / [(1-x)^2 * (1-xy) ]. - R. Stephan, Jan 25 2005
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EXAMPLE
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0; 1,0; 2,1,0; 3,2,1,0; 4,3,2,1,0; ...
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MAPLE
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A025581 := n -> binomial(1+floor((1/2)+sqrt(2*(1+n))), 2) - (n+1);
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PROGRAM
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(PARI) a(n)=binomial(1+floor(1/2+sqrt(2+2*n)), 2)-(n+1) /* produces a(n) */
(PARI) t1(n)=binomial(floor(3/2+sqrt(2+2*n)), 2)-(n+1) /* A025581 */
(PARI) t2(n)=n-binomial(floor(1/2+sqrt(2+2*n)), 2) /* A002262 */
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CROSSREFS
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A004736(n+1)=1+A025581(n)
Cf. A025669, A025676, A025683, A002262, A004736.
Sequence in context: A117901 A074984 A112658 this_sequence A025669 A025676 A025683
Adjacent sequences: A025578 A025579 A025580 this_sequence A025582 A025583 A025584
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KEYWORD
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nonn,tabl,easy,nice
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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