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Search: id:A124725
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| A124725 |
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Triangle read by rows: T(n,k)=binom(n,k) + binom(n,k+2) (0<=k<=n). |
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+0
3
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| 1, 1, 1, 2, 2, 1, 4, 4, 3, 1, 7, 8, 7, 4, 1, 11, 15, 15, 11, 5, 1, 16, 26, 30, 26, 16, 6, 1, 22, 42, 56, 56, 42, 22, 7, 1, 29, 64, 98, 112, 98, 64, 29, 8, 1, 37, 93, 162, 210, 210, 162, 93, 37, 9, 1, 46, 130, 255, 372, 420, 372, 255, 130, 46, 10, 1, 56, 176, 385, 627, 792, 792, 627
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Binomial transform of the infinite tridiagonal matrix with main diagonal, (1,1,1...), subdiagonal, (0,0,0...) and subsubdiagonal, (1,1,1...). Sum of entries in row n = 2^(n+1)-n-1=A000325(n+1).
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EXAMPLE
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Row 3 = (4, 4, 3, 1), then row 4 = (7, 8, 7, 4, 1).
First few rows of the triangle are:
1;
1, 1;
2, 2, 1;
4, 4, 3, 1;
7, 8, 7, 4, 1;
11, 15, 15, 11, 5, 1;
16, 26, 30, 26, 16, 6, 1;
...
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MAPLE
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T:=(n, k)->binomial(n, k)+binomial(n, k+2): for n from 0 to 12 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A098574, A000125, A055795, A027660, A055796, A002663.
Cf. A000325.
Sequence in context: A092848 A128111 A107356 this_sequence A106522 A128175 A104040
Adjacent sequences: A124722 A124723 A124724 this_sequence A124726 A124727 A124728
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson & Roger L. Bagula (qntmpkt(AT)yahoo.com), Nov 05 2006
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 29 2006
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