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A101493
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Triangle read by rows: T(n,k)=(n+1)*(2*(n+1)-1)-k*(2*k-1).
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1
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1, 6, 5, 15, 14, 9, 28, 27, 22, 13, 45, 44, 39, 30, 17, 66, 65, 60, 51, 38, 21, 91, 90, 85, 76, 63, 46, 25, 120, 119, 114, 105, 92, 75, 54, 29, 153, 152, 147, 138, 125, 108, 87, 62, 33, 190, 189, 184, 175, 162, 145, 124, 99, 70, 37, 231, 230, 225, 216, 203, 186, 165, 140
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The triangle is generated from the product B*A 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)= n*(2*n-1) = A000384(n) (Hexagonal numbers)
since T(n,n) = 4*n+1 = A016813(n)
T(n,n)=4*n+1=A016813(n)
T(n+1,n)=8*n+6=A017137(n)
T(n+2,n)=12*n+3=A017557(n)
T(n,n)*T(n,0) = (n+1)*(2*n+1)*(4*n+1) = A079588(n)
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EXAMPLE
| Triangle begins:
1;
6, 5;
15, 14, 9;
28, 27, 22, 13;
45, 44, 39, 30, 17;
66, 65, 60, 51, 38, 21;
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PROG
| (PARI) T(n, k)=if(k>n, 0, (n+1)*(2*(n+1)-1)-k*(2*k-1)) for(i=0, 10, for(j=0, i, print1(T(i, j), ", ")); print())
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CROSSREFS
| Row sums give 10-gonal pyramidal numbers: n(n+1)(8n-5)/6 = A007585(n+1).
Cf. A101492 (for product A*B), A007585, A000384.
Sequence in context: A120114 A123168 A119636 * A188067 A039668 A143130
Adjacent sequences: A101490 A101491 A101492 * A101494 A101495 A101496
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KEYWORD
| nonn,tabl
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AUTHOR
| Lambert Klasen (lambert.klasen(AT)gmx.de) and Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 21 2005
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