A100852 Triangle read by rows: T(n,k) = 2^k * 3^n, 0 <= k <= n.

1, 3, 6, 9, 18, 36, 27, 54, 108, 216, 81, 162, 324, 648, 1296, 243, 486, 972, 1944, 3888, 7776, 729, 1458, 2916, 5832, 11664, 23328, 46656, 2187, 4374, 8748, 17496, 34992, 69984, 139968, 279936, 6561, 13122, 26244, 52488, 104976, 209952, 419904, 839808

Offset

0,2

Comments

T(n,0) = A000244(n); T(n,n) = A000400(n) = A100851(n,n);

T(n,1) = A008776(n) for n>0;

T(n,2) = A003946(n+1) for n>1;

T(n,3) = A005051(n+1) for n>2;

T(n,n-1) = A081341(n+1) for n>0;

row sums give A016137.

Links

Michael De Vlieger, Table of n, a(n) for n = 0..10010 (Rows 0 <= n <= 140).

Eric Weisstein's World of Mathematics, Smooth Number

Formula

G.f.: 1/((1 - 3*x)(1 - 6*x*y)). - Ilya Gutkovskiy, Jun 03 2017

Example

Triangle begins:
   1;
   3,   6;
   9,  18,  36;
  27,  54, 108, 216;
  81, 162, 324, 648, 1296;
...

Mathematica

Table[2^k*3^n, {n, 0, 140}, {k, 0, n}] // Flatten (* Michael De Vlieger, Mar 06 2017 *)

Prog

(PARI) for(n=0, 8, for(k=0, n, print1(2^k*3^n", "))) \\ Satish Bysany, Mar 06 2017

Crossrefs

Cf. A100851, A003586, A065333(T(n, k))=1.

Sequence in context: A025614 A182751 A057576 * A059006 A342596 A363124

Adjacent sequences: A100849 A100850 A100851 * A100853 A100854 A100855

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Nov 20 2004

Status

approved