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Search: id:A101492
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| A101492 |
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Triangle read by rows: T(n,k)=(n+1-k)*(4*k+1). |
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+0
2
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| 1, 2, 5, 3, 10, 9, 4, 15, 18, 13, 5, 20, 27, 26, 17, 6, 25, 36, 39, 34, 21, 7, 30, 45, 52, 51, 42, 25, 8, 35, 54, 65, 68, 63, 50, 29, 9, 40, 63, 78, 85, 84, 75, 58, 33, 10, 45, 72, 91, 102, 105, 100, 87, 66, 37, 11, 50, 81, 104, 119, 126, 125, 116, 99, 74, 41, 12, 55, 90, 117
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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The triangle is generated from the product A*B
of the infinite lower triangular matrices A =
1 0 0 0...
1 1 0 0...
1 1 1 0...
1 1 1 1...
... and B =
1 0 0 0...
1 5 0 0...
1 5 9 0...
1 5 9 13...
...
T(n+0,0)= 1*n=A000027(n+1)
T(n+0,1)= 5*n=A008587(n)
T(n+1,2)= 9*n=A008591(n)
T(n+2,3)=13*n=A008595(n)
so, for example
T(n,n)=4*n+1=A016813(n)
T(n+1,n)=8*n+2=A017089(n)
T(n,0)*T(n,1)/10 = A000217(n) (triangular numbers)
T(n,n)*T(n,0) = A001107(n+1) (10-gonal numbers: 4n^2 - 3n)
T(n,n)*T(n,1)/5 = A007742(n)
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PROGRAM
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(PARI) T(n, k) = if(k>n, 0, (n-k+1)*(4*k+1)) for(i=0, 10, for(j=0, i, print1(T(i, j), ", ")); print())
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CROSSREFS
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Row sums give hexagonal pyramidal numbers A002412.
Cf. A101493 for product B*A, A002412.
Sequence in context: A078386 A163254 A143121 this_sequence A138765 A097753 A120860
Adjacent sequences: A101489 A101490 A101491 this_sequence A101493 A101494 A101495
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KEYWORD
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nonn,tabl
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AUTHOR
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Lambert Klasen (lambert.klasen(AT)gmx.de) and Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 21 2005
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