A131063 Triangle read by rows: T(n,k) = 5*binomial(n,k) - 4 for 0 <= k <= n.

1, 1, 1, 1, 6, 1, 1, 11, 11, 1, 1, 16, 26, 16, 1, 1, 21, 46, 46, 21, 1, 1, 26, 71, 96, 71, 26, 1, 1, 31, 101, 171, 171, 101, 31, 1, 1, 36, 136, 276, 346, 276, 136, 36, 1, 1, 41, 176, 416, 626, 626, 416, 176, 41, 1, 1, 46, 221, 596, 1046, 1256, 1046, 596, 221, 46, 1

Offset

0,5

Comments

Row sums = A131064: (1, 2, 8, 24, 60, 136, 292, ...), the binomial transform of (1, 1, 5, 5, 5, ...).

Links

Muniru A Asiru, Rows n=0..100 of triangle, flattened

Formula

G.f.: (1-z-t*z+5*t*z^2)/((1-z)*(1-t*z)*(1-z-t*z)). - Emeric Deutsch, Jun 20 2007

Example

First few rows of the triangle:
  1;
  1,  1;
  1,  6,  1;
  1, 11, 11,  1;
  1, 16, 26, 16,  1;
  1, 21, 46, 46, 21,  1;
  1, 26, 71, 96, 71, 26,  1;
  ...

Maple

T := proc (n, k) if k <= n then 5*binomial(n, k)-4 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[5*Binomial[n, k] -4, {n, 0, 10}, {k, 0, n}]//Flatten (* G. C. Greubel, Mar 12 2020 *)

Prog

(GAP) Print(Flat(List([0..10], n->List([0..n], k->5*Binomial(n, k)-4)))); # Muniru A Asiru, Feb 21 2019
(Magma) [5*Binomial(n, k) -4: k in [0..n], n in [0..10]]; // G. C. Greubel, Mar 12 2020
(Sage) [[5*binomial(n, k) -4 for k in (0..n)] for n in (0..10)] # G. C. Greubel, Mar 12 2020

Crossrefs

Cf. A109128, A123203, A131060, A131061, A131064, A131065, A131066, A131067, A131068.

Sequence in context: A144395 A046621 A046617 * A081579 A295707 A146772

Adjacent sequences: A131060 A131061 A131062 * A131064 A131065 A131066

Keyword

nonn,tabl

Author

Gary W. Adamson, Jun 13 2007

Extensions

More terms from Emeric Deutsch, Jun 20 2007

Status

approved