A154919 Triangle, read by rows, T(n, k) = binomial(3*n, 2*k) + binomial(3*n, 2*(n-k)).

2, 4, 4, 16, 30, 16, 85, 162, 162, 85, 496, 990, 990, 990, 496, 3004, 6540, 6370, 6370, 6540, 3004, 18565, 43911, 46818, 37128, 46818, 43911, 18565, 116281, 294140, 358701, 257754, 257754, 358701, 294140, 116281, 735472, 1961532, 2714782, 2095852, 1470942, 2095852, 2714782, 1961532, 735472

Offset

0,1

Comments

Row sums are: {2, 8, 62, 494, 3962, 31828, 255716, 2053752, 16486218, 132274304, 1060792742, ...}.

Links

G. C. Greubel, Rows n = 0..100 of triangle, flattened

Formula

T(n, k) = binomial(3*n, 2*k) + binomial(3*n, 2*(n-k)).

Example

Triangle begins as:
      2;
      4,     4;
     16,    30,    16;
     85,   162,   162,    85;
    496,   990,   990,   990,   496;
   3004,  6540,  6370,  6370,  6540,  3004;
  18565, 43911, 46818, 37128, 46818, 43911, 18565;

Maple

b:=binomial; seq(seq( b(3*n, 2*k) + b(3*n, 2*(n-k)), k=0..n), n=0..10); # G. C. Greubel, Dec 02 2019

Mathematica

Table[Binomial[3*n, 2*k] +Binomial[3*n, 2*(n-k)], {n, 0, 10}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Dec 02 2019 *)

Prog

(PARI) T(n, k) = my(b=binomia); b(3*n, 2*k) + b(3*n, 2*(n-k)); \\ G. C. Greubel, Dec 02 2019
(Magma) B:=Binomial; [B(3*n, 2*k) + B(3*n, 2*(n-k)): k in [0..n], n in [0..10]]; // G. C. Greubel, Dec 02 2019
(Sage) b=binomial; [[b(3*n, 2*k) + b(3*n, 2*(n-k)) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Dec 02 2019
(GAP) B:=Binomial;; Flat(List([0..10], n-> List([0..n], k-> B(3*n, 2*k) + B(3*n, 2*(n-k)) ))); # G. C. Greubel, Dec 02 2019

Crossrefs

Sequence in context: A230874 A349452 A176739 * A019230 A298148 A088042

Adjacent sequences: A154916 A154917 A154918 * A154920 A154921 A154922

Keyword

nonn,tabl

Author

Roger L. Bagula, Jan 17 2009

Extensions

Edited by G. C. Greubel, Dec 02 2019

Status

approved