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A294317
Triangle read by rows: T(n, k) = 2*n-k, k <= n.
4
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
0,2
LINKS
Thomas H. Sidebotham, The A to Z of Mathematics: A Basic Guide, John Wiley & Sons, p. 181, (2003) ISBN 9780471461630.
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
EXAMPLE
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;
...
MATHEMATICA
Column[Table[2*n-k, {n, 0, 10}, {k, 0, n}], Center]
PROG
(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))
(GAP) A294317 := Flat(List([0..149], n->List([0..n], k->2*n-k))); # Muniru A Asiru, Dec 29 2017
CROSSREFS
KEYWORD
nonn,tabl,easy
AUTHOR
Kolosov Petro, Oct 28 2017
EXTENSIONS
Edited by Wolfdieter Lang, Dec 08 2017
STATUS
approved