A029656 Numbers in the (2,1)-Pascal triangle A029653 that are different from 1.

2, 2, 3, 2, 5, 4, 2, 7, 9, 5, 2, 9, 16, 14, 6, 2, 11, 25, 30, 20, 7, 2, 13, 36, 55, 50, 27, 8, 2, 15, 49, 91, 105, 77, 35, 9, 2, 17, 64, 140, 196, 182, 112, 44, 10, 2, 19, 81, 204, 336, 378, 294, 156, 54, 11, 2, 21, 100, 285, 540, 714, 672, 450, 210, 65, 12, 2, 23, 121, 385

Offset: 1

Author

Mohammad K. Azarian

Keywords

• nonn
• tabl

Examples

			Triangle begins:
  2;
  2,  3;
  2,  5,  4;
  2,  7,  9,  5;
  2,  9, 16, 14,  6;
  2, 11, 25, 30, 20,  7;
  ...
		

References

• D. M. Bressoud, Proofs and Confirmations, Camb. Univ. Press, 1999; triangle on page 6, numerators.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..11325 (rows 1 <= n <= 150)
• Eric Weisstein's World of Mathematics, Alternating Sign Matrix.
• D. Zeilberger, Dave Robbins's Art of Guessing, Adv. in Appl. Math. 34 (2005), 939-954.

Crossrefs

Cf. A048601, A029638.

Programs

Mathematica

Table[(Binomial[n + 2, k + 1] + Binomial[n + 1, k] + Binomial[n, k] - Binomial[n, k + 1])/2, {n, 0, 11}, {k, 0, n}] // Flatten (* Michael De Vlieger, Jun 29 2018 *)

Formula

From Thomas Baruchel, Jun 26 2018: (Start)

a(n,k) = (binomial(n+2,k+1) + binomial(n+1,k) + binomial(n,k) - binomial(n,k+1))/2.

a(n,k) = binomial(n-1,k-1) + binomial(n-1,k) + binomial(n,k-1) + binomial(n,k). (End)

Extensions

More terms from James Sellers