A294317 Triangle read by rows: T(n, k) = 2*n-k, k <= n.

0, 2, 1, 4, 3, 2, 6, 5, 4, 3, 8, 7, 6, 5, 4, 10, 9, 8, 7, 6, 5, 12, 11, 10, 9, 8, 7, 6, 14, 13, 12, 11, 10, 9, 8, 7, 16, 15, 14, 13, 12, 11, 10, 9, 8, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10

Offset: 0

Author

Kolosov Petro, Oct 28 2017

Keywords

• nonn
• tabl
• easy

Examples

			Triangle begins:
   0;
   2,  1;
   4,  3,  2;
   6,  5,  4,  3;
   8,  7,  6,  5,  4;
  10,  9,  8,  7,  6,  5;
  12, 11, 10,  9,  8,  7,  6;
  14, 13, 12, 11, 10,  9,  8,  7;
  16, 15, 14, 13, 12, 11, 10,  9,  8;
  18, 17, 16, 15, 14, 13, 12, 11, 10, 9;
  20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10;
  ...
		

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..100000
• Thomas H. Sidebotham, The A to Z of Mathematics: A Basic Guide, John Wiley & Sons, p. 181, (2003) ISBN 9780471461630.

Crossrefs

Cf. A001477, A005408, A005843, A287326.

Programs

GAP

A294317 := Flat(List([0..149],n->List([0..n],k->2*n-k))); # Muniru A Asiru, Dec 29 2017

Mathematica

Column[Table[2*n-k, {n, 0, 10}, {k, 0, n}], Center]

Python

def f(x):
    a=[]
    for k in range(x):
        for m in range (k+1):
            a.append(2*k-m)
    return a
print(f(10))

Formula

T(n, k) = 2*n - k, 0 <= k <= n.

T(n, 2*m) = A005843(n), n >= m >= 0 (even-indexed columns).

T(n, 2*m+1) = A005408(n), n >= m >= 0 (odd-indexed columns).

T(n, n-m) = A001477(n+m), n >= m >= 0 (diagonals m >= 0).

2*A287326(n, k) = A287326(T(n, k),k) + A287326(T(n, k),0).

G.f.: x*(2 + y - 3*x*y)/((1 - x)^2*(1 - x*y)^2). - Stefano Spezia, Sep 14 2024

Extensions

Edited by Wolfdieter Lang, Dec 08 2017