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Search: id:A087755
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| A087755 |
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Triangle read by rows: Stirling numbers of the first kind (A008275) mod 2. |
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+0
2
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| 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1
(list; table; graph; listen)
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OFFSET
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1,1
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COMMENT
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Essentially also parity of Mitrinovic's triangles A049458, A049460, A051339, A051380.
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FORMULA
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T(n, k) = A087748(n, k) = A008275(n, k) mod 2 = A047999([n/2], k-[(n+1)/ 2]) = T(n-2, k-2) XOR T(n-2, k-1) with T(1, 1) = T(2, 1) = T(2, 2) = 1; T(2n, k) = T(2n-1, k-1) XOR T(2n-1, k); T(2n+1, k) = T(2n, k-1). - Henry Bottomley (se16(AT)btinternet.com), Dec 01 2003
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EXAMPLE
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Triangle begins:
1
1 1
0 1 1
0 1 0 1
0 0 1 0 1
0 0 1 1 1 1
0 0 0 1 1 1 1
0 0 0 1 0 0 0 1
0 0 0 0 1 0 0 0 1
0 0 0 0 1 1 0 0 1 1
0 0 0 0 0 1 1 0 0 1 1
0 0 0 0 0 1 0 1 0 1 0 1
0 0 0 0 0 0 1 0 1 0 1 0 1
0 0 0 0 0 0 1 1 1 1 1 1 1 1
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PROGRAM
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(PARI) p = 2; s=14; S1T = matrix(s, s, n, k, if(k==1, (-1)^(n-1)*(n-1)!)); for(n=2, s, for(k=2, n, S1T[n, k]=-(n-1)*S1T[n-1, k]+S1T[n-1, k-1]));
S1TMP = matrix(s, s, n, k, S1T[n, k]%p);
for(n=1, s, for(k=1, n, print1(S1TMP[n, k], " ")); print()) /* Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Oct 17 2009 */
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CROSSREFS
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Sequence in context: A130304 A118274 A080909 this_sequence A050072 A156707 A131309
Adjacent sequences: A087752 A087753 A087754 this_sequence A087756 A087757 A087758
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Oct 02 2003
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EXTENSIONS
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Edited and extended by Henry Bottomley (se16(AT)btinternet.com), Dec 01 2003
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