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A101468 Triangle read by rows: T(n,k)=(n+1-k)*(3*k+1). 1
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; text; internal format)
OFFSET
0,2
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.
LINKS
EXAMPLE
Triangle begins:
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, etc.
[Bruno Berselli, Feb 10 2014]
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}]] (* Robert G. Wilson v, Jan 21 2005 *)
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())
CROSSREFS
Cf. A095871 (product B*A), A002411.
Sequence in context: A324931 A168521 A244982 * A188866 A235486 A066194
KEYWORD
nonn,tabl
AUTHOR
Lambert Klasen (lambert.klasen(AT)gmx.de) and Gary W. Adamson, Jan 21 2005
STATUS
approved

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Last modified March 29 11:14 EDT 2024. Contains 371278 sequences. (Running on oeis4.)