A131065 Triangle read by rows: T(n,k) = 6*binomial(n,k) - 5 for 0 <= k <= n.

1, 1, 1, 1, 7, 1, 1, 13, 13, 1, 1, 19, 31, 19, 1, 1, 25, 55, 55, 25, 1, 1, 31, 85, 115, 85, 31, 1, 1, 37, 121, 205, 205, 121, 37, 1, 1, 43, 163, 331, 415, 331, 163, 43, 1, 1, 49, 211, 499, 751, 751, 499, 211, 49, 1, 1, 55, 265, 715, 1255, 1507, 1255, 715, 265, 55, 1

Offset: 0

Author

Gary W. Adamson, Jun 13 2007

Keywords

• nonn
• tabl

Comments

Row sums = A131066.

The matrix inverse starts:

1;

-1, 1;

6, -7, 1;

-66, 78, -13, 1;

1086, -1284, 216, -19, 1;

-23826, 28170, -4740, 420, -25, 1;

653406, -772536, 129990, -11520, 690, -31, 1; - R. J. Mathar, Mar 12 2013

Examples

			First few rows of the triangle are:
  1;
  1,  1;
  1,  7,  1;
  1, 13, 13,  1;
  1, 19, 31, 19,  1;
  1, 25, 55, 55, 25, 1;
...
		

Links

• Indranil Ghosh, Rows 0..120 of triangle, flattened

Crossrefs

Cf. A109128, A123203, A131060, A131061, A131063, A131064, A131066, A131067, A131068.

Programs

Magma

[6*Binomial(n,k) -5: k in [0..n], n in [0..10]]; // G. C. Greubel, Mar 12 2020

Maple

T := proc (n, k) if k <= n then 6*binomial(n, k)-5 else 0 end if end proc: for n from 0 to 10 do seq(T(n, k), k = 0 .. n) end do; # Emeric Deutsch, Jun 20 2007

Mathematica

Table[6*Binomial[n,k]-5,{n,0,15},{k,0,n}]//Flatten (* Harvey P. Dale, May 15 2016 *)

Sage

[[6*binomial(n,k) -5 for k in (0..n)] for n in (0..10)] # G. C. Greubel, Mar 12 2020

Formula

G.f.: (1-z-t*z+6*t*z^2)/((1-z)*(1-t*z)*(1-z-t*z)). - Emeric Deutsch, Jun 20 2007

Extensions

More terms from Emeric Deutsch, Jun 20 2007