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Search: id:A111960
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| 1, 1, 1, 3, 2, 1, 7, 7, 3, 1, 19, 20, 12, 4, 1, 51, 61, 40, 18, 5, 1, 141, 182, 135, 68, 25, 6, 1, 393, 547, 441, 251, 105, 33, 7, 1, 1107, 1640, 1428, 888, 420, 152, 42, 8, 1, 3139, 4921, 4572, 3076, 1596, 654, 210, 52, 9, 1, 8953, 14762, 14535, 10456, 5880, 2652, 966, 280
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Factors as (1/(1-x), x/(1-x))*(1/sqrt(1-4x^2), x/sqrt(1-4x^2)) [A007318*A111959]. Row sums are A111961. Diagonal sums are A111962. Inverse is A111963.
Equals ((1-x^2)/(1+x+x^2),x/(1+x+x^2))^{-1}*(1,x/(1-x^2))=A094531*(1,x/(1-x^2)). [From Paul Barry (pbarry(AT)wit.ie), May 12 2009]
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FORMULA
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Riordan array (1/sqrt(1-2x-3x^2), x/sqrt(1-2x-3x^2)); Number triangle T(n, k)=sum{j=0..n, C(n, j)*C((j-1)/2, (j-k)/2)*2^(j-k)*(1+(-1)^(j-k))/2};
G.f.: 1/(1-xy-x-2x^2/(1-x-x^2/(1-x-x^2/(1-x-x^2/(1-... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), May 12 2009]
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EXAMPLE
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Triangle begins
1;
1,1;
3,2,1;
7,7,3,1;
19,20,12,4,1;
51,61,40,18,5,1;
Contribution from Paul Barry (pbarry(AT)wit.ie), May 12 2009: (Start)
Production matrix is
1, 1,
2, 1, 1,
0, 2, 1, 1,
-2, 0, 2, 1, 1,
0, -2, 0, 2, 1, 1,
4, 0, -2, 0, 2, 1, 1 (End)
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CROSSREFS
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Sequence in context: A115990 A094531 A161009 this_sequence A130462 A059380 A145035
Adjacent sequences: A111957 A111958 A111959 this_sequence A111961 A111962 A111963
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Aug 23 2005
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