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A101493
Triangle read by rows: T(n,k) = (n+1)*(2*(n+1)-1) - k*(2*k-1).
2
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, 111, 78, 41
OFFSET
0,2
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).
EXAMPLE
Triangle begins:
1;
6, 5;
15, 14, 9;
28, 27, 22, 13;
45, 44, 39, 30, 17;
66, 65, 60, 51, 38, 21;
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())
(GAP) Flat(List([0..10], n->List([0..n], k->(n+1)*(2*n+1)-k*(2*k-1)))); # Muniru A Asiru, Mar 05 2019
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: A123168 A119636 A300750 * A347276 A188067 A039668
KEYWORD
nonn,tabl
AUTHOR
Lambert Klasen (lambert.klasen(AT)gmx.de) and Gary W. Adamson, Jan 21 2005
STATUS
approved