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Search: id:A114278
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| A114278 |
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A triangle generated by a family of Sierpinski-triangle related polynomials. |
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+0
3
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| 1, 1, 1, 1, 3, 1, 1, 5, 3, 1, 1, 7, 7, 5, 1, 1, 9, 13, 15, 5, 1, 1, 11, 21, 35, 15, 7, 1, 1, 13, 31, 69, 35, 27, 7, 1, 1, 15, 43, 121, 71, 77, 29, 9, 1, 1, 17, 57, 195, 131, 183, 91, 45, 9, 1, 1, 19, 73, 295, 225, 385, 239, 165, 45, 11, 1
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Inverse has row sums 0^n (conjecture). Row sums are A114279.
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FORMULA
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Column k has g.f. x^k*sum{j=0..k, mod(C(k, j), 2)*x^j}/(1-x)^(k+1); Column k has g.f. x^k*sum{j=0..k, A001316(j)*A114280(k, j)*x^j/(1-x)^(j+1)}.
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EXAMPLE
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Triangle begins
1;
1, 1;
1, 3, 1;
1, 5, 3, 1;
1, 7, 7, 5, 1;
1, 9,13,15, 5, 1;
1,11,21,35,15, 7, 1;
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CROSSREFS
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Adjacent sequences: A114275 A114276 A114277 this_sequence A114279 A114280 A114281
Sequence in context: A135228 A021325 A131247 this_sequence A134836 A131767 A026780
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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), Nov 20 2005
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