

A131923


Triangle read by rows: T(n,k) = binomial(n,k) + n.


2



1, 2, 2, 3, 4, 3, 4, 6, 6, 4, 5, 8, 10, 8, 5, 6, 10, 15, 15, 10, 6, 7, 12, 21, 26, 21, 12, 7, 8, 14, 28, 42, 42, 28, 14, 8, 9, 16, 36, 64, 78, 64, 36, 16, 9, 10, 18, 45, 93, 135, 135, 93, 45, 18, 10, 11, 20, 55, 130, 220, 262, 220, 130, 55, 20, 11, 12, 22, 66
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


COMMENTS

Row sums = A131924: (1, 4, 10, 20, 36, 62, 106, 184, ...).


LINKS



FORMULA



EXAMPLE

First few rows of the triangle are:
1;
2, 2;
3, 4, 3;
4, 6, 6, 4;
5, 8, 10, 8, 5;
6, 10, 15, 15, 10, 6;
7, 12, 21, 26, 21, 12, 7;
8, 14, 28, 42, 42, 28, 14, 8;
9, 16, 36, 64, 78, 64, 36, 16, 9;
10, 18, 45, 93, 135, 135, 93, 45, 18, 10;
...


MATHEMATICA

T[n_, m_] = Binomial[n, m] + n; Table[Table[T[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%] (* Roger L. Bagula, Jul 30 2008 *)


PROG

(GAP) a:=Flat(List([0..10], n>List([0..n], k>Binomial(n, k)+n))); # Muniru A Asiru, Jul 16 2018
(Magma) /* As triangle */ [[Binomial(n, k) + n: k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, Jul 17 2018


CROSSREFS



KEYWORD



AUTHOR



EXTENSIONS



STATUS

approved



