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Search: id:A096038
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| A096038 |
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Triangle T(n,m) = (3*n^2-3*m^2+5*m-4+n)/2 read by rows. |
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+0
4
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| 1, 6, 4, 14, 12, 7, 25, 23, 18, 10, 39, 37, 32, 24, 13, 56, 54, 49, 41, 30, 16, 76, 74, 69, 61, 50, 36, 19, 99, 97, 92, 84, 73, 59, 42, 22, 125, 123, 118, 110, 99, 85, 68, 48, 25, 154, 152, 147, 139, 128, 114, 97, 77, 54, 28, 186, 184, 179, 171, 160, 146, 129, 109, 86, 60, 31, 221
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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The triangle is obtained by subtracting the triangle A094930 from
its square root (also described in A094930) and then dividing each element of column m through 3*m-1.
For the first three rows n=1 to 3 this yields for example:
4;.................2;............2......................1;
14,25;......minus..2,5;.......=..12,20;......->.divide..6,4;
30,65,64;..........2,5,8;........28,60,56;..............14;12,7;
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FORMULA
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T(n,1) = A095794(n).
T(n,n) = 3*n-2.
T(n,m) = A094930(n,m)/(3*m-1)-1.
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PROGRAM
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(Python) def A096038(n, m): ...return (3*n**2-3*m**2+5*m-4+n)/2 print( [A096038(n, m) for n in range(20) for m in range(1, n+1)] ) # R. J. Mathar, Oct 11 2009
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CROSSREFS
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Cf. A095794, A011379, A002411, A096037, A096036, A024212.
Sequence in context: A040032 A006582 A131828 this_sequence A083581 A160248 A107983
Adjacent sequences: A096035 A096036 A096037 this_sequence A096039 A096040 A096041
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 17 2004
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EXTENSIONS
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Edited, T(3,2) corrected, and extended by R. J. Mathar, (mathar(AT)strw.leidenuniv.nl), Oct 11 2009
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