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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
A007318 + A002024 - A000012 = A007318 + A003056 as infinite lower triangular matrices. A002024 = (1; 2,2; 3,3,3;...); A007318 = Pascal's triangle and A000012 = (1; 1,1; 1,1,1;...).
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
(PARI) T(n, k) = binomial(n, k) + n \\ Charles R Greathouse IV, Oct 16 2013
(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
Sequence in context: A319840 A368310 A003991 * A119457 A241356 A065157
KEYWORD
nonn,tabl,easy
AUTHOR
Gary W. Adamson, Jul 29 2007
EXTENSIONS
Edited, changing formula by Roger L. Bagula, Jul 30 2008
New name from Franklin T. Adams-Watters, Oct 16 2013
Terms 54 onwards from Muniru A Asiru, Jul 16 2018
STATUS
approved

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Last modified March 1 05:26 EST 2024. Contains 370430 sequences. (Running on oeis4.)