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Search: id:A072405
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| A072405 |
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Triangle of C(n,k)-C(n-2,k-1). |
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+0
9
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| 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 4, 3, 1, 1, 4, 7, 7, 4, 1, 1, 5, 11, 14, 11, 5, 1, 1, 6, 16, 25, 25, 16, 6, 1, 1, 7, 22, 41, 50, 41, 22, 7, 1, 1, 8, 29, 63, 91, 91, 63, 29, 8, 1, 1, 9, 37, 92, 154, 182, 154, 92, 37, 9, 1, 1, 10, 46, 129, 246, 336, 336, 246, 129, 46, 10, 1, 1, 11, 56
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OFFSET
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0,8
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COMMENT
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Starting 1,0,1,1,1,... this is the Riordan array ((1-x+x^2)/(1-x),x/(1-x)). Its diagonal sums are A006355. Its inverse is A106509. - Paul Barry (pbarry(AT)wit.ie), May 04 2005
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FORMULA
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T(n, k)=T(n-1, k-1)+T(n-1, k) starting with T(2, 0)=T(2, 1)=T(2, 2)=1.
G.f.: (1-x^2y) / [1-x(1+y)]. - R. Stephan, Jan 31 2005
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EXAMPLE
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Rows start: 1; 1,1; 1,1,1 (the key row for applying the recurrence); 1,2,2,1; 1,3,4,3,1; 1,4,7,7,4,1; 1,5,11,14,11,5,1 etc.
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CROSSREFS
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Row sums give essentially A003945, A007283, or A042950. Cf. A072406 for number of odd terms in each row.
Cf. A028262.
Sequence in context: A086461 A047089 A122218 this_sequence A146565 A115594 A086623
Adjacent sequences: A072402 A072403 A072404 this_sequence A072406 A072407 A072408
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Jun 16 2002
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