A101493 -id:A101493 - cp's OEIS frontend

A101492 Triangle read by rows: T(n,k) = (n-k+1)(4k+1).

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

Offset: 0

Lambert Klasen (lambert.klasen(AT)gmx.de) and Gary W. Adamson, Jan 21 2005

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: 4*n^2 - 3*n),
T(n,n)*T(n,1)/5 = A007742(n).

Muniru A Asiru, Rows n=0..150 of triangle, flattened

Row sums give hexagonal pyramidal numbers A002412.

Cf. A101493 for product B*A, A002412.

Flat(List([0..11],n->List([0..n],k->(n+1-k)*(4*k+1)))); # Muniru A Asiru, Mar 07 2019

[[(n+1-k)*(4*k+1): k in [0..n]]: n in [0..10]]; // G. C. Greubel, Mar 07 2019

Flatten[Table[(n+1-k)(4k+1),{n,0,15},{k,0,n}]] (* Harvey P. Dale, Jun 09 2011 *)

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())

[[(n-k+1)*(4*k+1) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Mar 07 2019

cp's OEIS Frontend

A101492 Triangle read by rows: T(n,k) = (n-k+1)(4k+1).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

GAP

Magma

Mathematica

PARI

Sage

cp's OEIS Frontend

A101492 Triangle read by rows: T(n,k) = (n-k+1)*(4*k+1).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

GAP

Magma

Mathematica

PARI

Sage

A101492 Triangle read by rows: T(n,k) = (n-k+1)(4k+1).