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Search: id:A131087
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| A131087 |
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Triangle read by rows: T(n,k)=2*binom(n,k)-[1+(-1)^(n-k)]/2 (0<=k<=n). |
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+0
2
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| 1, 2, 1, 1, 4, 1, 2, 5, 6, 1, 1, 8, 11, 8, 1, 2, 9, 20, 19, 10, 1, 1, 12, 29, 40, 29, 12, 1, 2, 13, 42, 69, 70, 41, 14, 1, 1, 16, 55, 112, 139, 112, 55, 16, 1, 2, 17, 72, 167, 252, 251, 168, 71, 18, 1, 1, 20, 89, 240, 419, 504, 419, 240, 89, 20, 1, 2, 21, 110, 329, 660, 923, 924
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Row sums = A084174: (1, 3, 6, 14, 29,...).
2*A007318 - A128174 as infinite lower triangular matrices. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 21 2007
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FORMULA
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G.f.=G(t,z)=(1+z-tz-2z^2+2tz^3)/[(1-z^2)(1-tz)(1-z-tz)]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 21 2007
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EXAMPLE
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First few rows of the triangle are:
1;
2, 1;
1, 4, 1;
2, 5, 6, 1;
1, 8, 11, 8, 1;
2, 9, 20, 19, 10, 1;
1, 12, 29, 40, 29, 12, 1;
...
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MAPLE
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T := proc (n, k) options operator, arrow; 2*binomial(n, k)-1/2-(1/2)*(-1)^(n-k) end proc; for n from 0 to 11 do seq(T(n, k), k = 0 .. n) end do; # yields sequence in triangular form - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 21 2007
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CROSSREFS
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Cf. A128174, A084174.
Sequence in context: A105477 A127709 A131350 this_sequence A105475 A144389 A136321
Adjacent sequences: A131084 A131085 A131086 this_sequence A131088 A131089 A131090
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 14 2007
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 21 2007
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