

A101492


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


2



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
(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 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) (10gonal numbers: 4*n^2  3*n),
T(n,n)*T(n,1)/5 = A007742(n).


LINKS

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


MATHEMATICA

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


PROG

(PARI) T(n, k) = if(k>n, 0, (nk+1)*(4*k+1));
for(i=0, 10, for(j=0, i, print1(T(i, j), ", ")); print())
(GAP) Flat(List([0..11], n>List([0..n], k>(n+1k)*(4*k+1)))); # Muniru A Asiru, Mar 07 2019
(Magma) [[(n+1k)*(4*k+1): k in [0..n]]: n in [0..10]]; // G. C. Greubel, Mar 07 2019
(Sage) [[(nk+1)*(4*k+1) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Mar 07 2019


CROSSREFS

Row sums give hexagonal pyramidal numbers A002412.
Cf. A101493 for product B*A, A002412.
Sequence in context: A163254 A277696 A143121 * A297442 A277709 A138765
Adjacent sequences: A101489 A101490 A101491 * A101493 A101494 A101495


KEYWORD

nonn,tabl


AUTHOR

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


STATUS

approved



