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A029656 Numbers in the (2,1)-Pascal triangle A029653 that are different from 1. 2
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

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)

EXAMPLE

Triangle begins:

  2;

  2,  3;

  2,  5,  4;

  2,  7,  9,  5;

  2,  9, 16, 14,  6;

  2, 11, 25, 30, 20,  7;

  ...

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 *)

CROSSREFS

Cf. A048601, A029638.

Sequence in context: A307687 A281121 A220949 * A121306 A073311 A003974

Adjacent sequences:  A029653 A029654 A029655 * A029657 A029658 A029659

KEYWORD

nonn,tabl

AUTHOR

Mohammad K. Azarian

EXTENSIONS

More terms from James A. Sellers

STATUS

approved

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Last modified October 22 07:53 EDT 2021. Contains 348160 sequences. (Running on oeis4.)