A194122 Triangular array: T(n,k) = C(n+4,k) + C(n+4,k+1) + C(n+4,k+2) + C(n+4,k+3) + C(n+4,k+4), 0 <= k <= n.

16, 31, 31, 57, 62, 57, 99, 119, 119, 99, 163, 218, 238, 218, 163, 256, 381, 456, 456, 381, 256, 386, 637, 837, 912, 837, 637, 386, 562, 1023, 1474, 1749, 1749, 1474, 1023, 562, 794, 1585, 2497, 3223, 3498, 3223, 2497, 1585, 794, 1093, 2379, 4082

Offset

0,1

Links

Muniru A Asiru, Rows n = 0..150 of triangle, flattened

Example

Triangle begins:
   16;
   31,  31;
   57,  62,  57;
   99, 119, 119,  99;
  163, 218, 238, 218, 163;

Maple

A194122 := proc(n, k) add(binomial(n+4, k+j), j=0..4) ; end proc: # R. J. Mathar, Aug 25 2011

Mathematica

T[n_, k_] := Sum[Binomial[n + 4, k + j], {j, 0, 4}]
Flatten[Table[T[n, k], {n, 0, 10}, {k, 0, n}]]
(* as a sequence *)
TableForm[Table[T[n, k], {n, 0, 10}, {k, 0, n}]]
(* as an array *)

Prog

(GAP) Flat(List([0..9], n->List([0..n], k->Sum([0..4], j->Binomial(n+4, k+j))))); # Muniru A Asiru, Mar 17 2019

Crossrefs

Cf. A192915.

Sequence in context: A186453 A129617 A221257 * A257349 A167997 A185979

Adjacent sequences: A194119 A194120 A194121 * A194123 A194124 A194125

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 16 2011

Status

approved