A154918 Triangle, read by rows, T(n, k) = binomial(4*n, 3*k) + binomial(4*n, 3*(n-k)).

2, 5, 5, 29, 112, 29, 221, 1144, 1144, 221, 1821, 12000, 16016, 12000, 1821, 15505, 127110, 206720, 206720, 127110, 15505, 134597, 1309528, 2838752, 2615008, 2838752, 1309528, 134597, 1184041, 13126386, 37818900, 37328655, 37328655, 37818900, 13126386, 1184041

Offset

0,1

Comments

Row sums are: {2, 10, 170, 2730, 43658, 698670, 11180762, 178915964, 2862907786,

45809074626, 732970281870, ...}.

Links

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

Formula

T(n, k) = binomial(4*n, 3*k) + binomial(4*n, 3*(n-k)).

Example

Triangle begins as:
      2;
      5,      5;
     29,    112,     29;
    221,   1144,   1144,    221;
   1821,  12000,  16016,  12000,   1821;
  15505, 127110, 206720, 206720, 127110, 15505;

Maple

b:=binomial; seq(seq( b(4*n, 3*k) + b(4*n, 3*(n-k)), k=0..n), n=0..10); # G. C. Greubel, Dec 02 2019

Mathematica

Table[Binomial[4*n, 3*k] +Binomial[4*n, 3*(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(4*n, 3*k) + b(4*n, 3*(n-k)); \\ G. C. Greubel, Dec 02 2019
(Magma) B:=Binomial; [B(4*n, 3*k) + B(4*n, 3*(n-k)): k in [0..n], n in [0..10]]; // G. C. Greubel, Dec 02 2019
(Sage) b=binomial; [[b(4*n, 3*k) + b(4*n, 3*(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(4*n, 3*k) + B(4*n, 3*(n-k)) ))); # G. C. Greubel, Dec 02 2019

Crossrefs

Sequence in context: A238879 A286258 A297446 * A176862 A352392 A176081

Adjacent sequences: A154915 A154916 A154917 * A154919 A154920 A154921

Keyword

nonn,tabl

Author

Roger L. Bagula, Jan 17 2009

Extensions

Edited by G. C. Greubel, Dec 02 2019

Status

approved