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A101468
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Triangle read by rows: T(n,k)=(n+1-k)*(3*k+1).
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0
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1, 2, 4, 3, 8, 7, 4, 12, 14, 10, 5, 16, 21, 20, 13, 6, 20, 28, 30, 26, 16, 7, 24, 35, 40, 39, 32, 19, 8, 28, 42, 50, 52, 48, 38, 22, 9, 32, 49, 60, 65, 64, 57, 44, 25, 10, 36, 56, 70, 78, 80, 76, 66, 50, 28, 11, 40, 63, 80, 91, 96, 95, 88, 75, 56, 31, 12, 44, 70, 90, 104, 112, 114
(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 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 4 0 0...
1 4 7 0...
1 4 7 10...
...
Row sums give pentagonal pyramidal numbers A002411 T(n+0,0)= 1*n=A000027(n) T(n+0,1)= 4*n=A008586(n) T(n+1,2)= 7*n=A008589(n) T(n+2,3)=10*n=A008592(n) ...
so for example T(n+1,n-0)=6*n+2=A016933(n) T(n+1,n-1)=9*n+3=A017197(n) T(n+2,n-1)=12*n+4=A017569(n)
T(n,0)*T(n,1) = A033996(n) (8 times triangular numbers)
T(n,n)*T(n,0) = A000567(n+1) (Octagonal numbers) etc.
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MATHEMATICA
| t[n_, k_] := If[n < k, 0, (3*k + 1)*(n - k + 1)]; Flatten[ Table[ t[n, k], {n, 0, 11}, {k, 0, n}]] (from Robert G. Wilson v Jan 21 2005)
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PROG
| (PARI) T(n, k)=if(k>n, 0, (n-k+1)*(3*k+1)) for(i=0, 10, for(j=0, i, print1(T(i, j), ", ")); print())
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CROSSREFS
| Cf. A095871 (product B*A), A002411.
Sequence in context: A124833 A181815 A168521 * A188866 A066194 A101283
Adjacent sequences: A101465 A101466 A101467 * A101469 A101470 A101471
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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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