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A124928 Triangle read by rows: T(n,0)=1, T(n,k)=3*binom(n,k) if k>=0 (0<=k<=n). 2
1, 1, 3, 1, 6, 3, 1, 9, 9, 3, 1, 12, 18, 12, 3, 1, 15, 30, 30, 15, 3, 1, 18, 45, 60, 45, 18, 3, 1, 21, 63, 105, 105, 63, 21, 3, 1, 24, 84, 168, 210, 168, 84, 24, 3, 1, 27, 108, 252, 378, 378, 252, 108, 27, 3, 1, 30, 135, 360, 630, 756, 630, 360, 135, 30, 3, 1, 33, 165, 495, 990 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Row sums = A033484: (1, 4, 10, 22, 46, 94...); 3*2^n - 2. Analogous triangle using (1,2,2,2...) as the main diagonal of M = A124927.

Except for the first column, entries in the Pascal triangle are tripled.

LINKS

Table of n, a(n) for n=0..70.

FORMULA

G.f.= G(t,z)=3/[1-(1+t)*z]-2/(1-z).

EXAMPLE

First few rows of the triangle are:

1;

1, 3;

1, 6, 3;

1, 9, 9, 3;

1, 12, 18, 12, 3;

1, 15, 30, 30, 15, 3;

1, 18, 45, 60, 45, 18, 3;

...

MAPLE

T:=proc(n, k) if k=0 then 1 else 3*binomial(n, k) fi end: for n from 0 to 12 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form

MATHEMATICA

Flatten[Table[If[k==0, 1, 3*Binomial[n, k]], {n, 0, 20}, {k, 0, n}]] (* Harvey P. Dale, Oct 19 2013 *)

CROSSREFS

Cf. A033484, A124927.

Sequence in context: A072361 A145366 A145367 * A249250 A122432 A131110

Adjacent sequences:  A124925 A124926 A124927 * A124929 A124930 A124931

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Nov 12 2006

EXTENSIONS

Edited by N. J. A. Sloane, Nov 29 2006

STATUS

approved

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Last modified February 18 23:26 EST 2018. Contains 299330 sequences. (Running on oeis4.)