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Search: id:A130154
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| A130154 |
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Triangle read by rows: T(n,k)=1 + 2(n-k)(k-1) (1<=k<=n). |
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+0
2
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| 1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 7, 9, 7, 1, 1, 9, 13, 13, 9, 1, 1, 11, 17, 19, 17, 11, 1, 1, 13, 21, 25, 25, 21, 13, 1, 1, 15, 25, 31, 33, 31, 25, 15, 1, 1, 17, 29, 37, 41, 41, 37, 29, 17, 1, 1, 19, 33, 43, 49, 51, 49, 43, 33, 19, 1, 1, 21, 37, 49, 57, 61, 61, 57, 49, 37, 21, 1, 1, 23, 41
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Column k, except for the initial k-1 0's, is an arithmetic progression with first term 1 and common difference 2(k-1). Row sums yield A116731. First column of the inverse matrix is A129779.
Studied by Paul Curtz circa 1993.
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FORMULA
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G.f.=G(t,z)=tz(3tz^2-z-tz+1)/[(1-tz)(1-z)]^2.
Equals = 2 * A077028 - A000012 as infinite lower triangular matrices. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 23 2007
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EXAMPLE
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Triangle starts:
1;
1,1;
1,3,1;
1,5,5,1;
1,7,9,7,1;
1,9,13,13,9,1;
1,11,17,19,17,11,1;
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MAPLE
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T:=proc(n, k) if k<=n then 2*(n-k)*(k-1)+1 else 0 fi end: for n from 1 to 14 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A116731, A129779.
Cf. A077028.
Sequence in context: A026703 A122917 A096583 this_sequence A134398 A026615 A026681
Adjacent sequences: A130151 A130152 A130153 this_sequence A130155 A130156 A130157
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KEYWORD
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nonn,tabl
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), May 22 2007
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