cp's OEIS Frontend

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

%I A294317 #51 Sep 14 2024 11:47:00
%S A294317 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,
%T A294317 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,
%U A294317 19,18,17,16,15,14,13,12,11,10
%N A294317 Triangle read by rows: T(n, k) = 2*n-k, k <= n.
%H A294317 Muniru A Asiru, <a href="/A294317/b294317.txt">Table of n, a(n) for n = 0..100000</a>
%H A294317 Thomas H. Sidebotham, <a href="https://books.google.com/books?id=VsAZa5PWLz8C&amp;pg=PA181">The A to Z of Mathematics: A Basic Guide</a>, John Wiley & Sons, p. 181, (2003) ISBN 9780471461630.
%F A294317 T(n, k) = 2*n - k, 0 <= k <= n.
%F A294317 T(n, 2*m) = A005843(n), n >= m >= 0 (even-indexed columns).
%F A294317 T(n, 2*m+1) = A005408(n), n >= m >= 0 (odd-indexed columns).
%F A294317 T(n, n-m) = A001477(n+m), n >= m >= 0 (diagonals m >= 0).
%F A294317 2*A287326(n, k) = A287326(T(n, k),k) + A287326(T(n, k),0).
%F A294317 G.f.: x*(2 + y - 3*x*y)/((1 - x)^2*(1 - x*y)^2). - _Stefano Spezia_, Sep 14 2024
%e A294317 Triangle begins:
%e A294317    0;
%e A294317    2,  1;
%e A294317    4,  3,  2;
%e A294317    6,  5,  4,  3;
%e A294317    8,  7,  6,  5,  4;
%e A294317   10,  9,  8,  7,  6,  5;
%e A294317   12, 11, 10,  9,  8,  7,  6;
%e A294317   14, 13, 12, 11, 10,  9,  8,  7;
%e A294317   16, 15, 14, 13, 12, 11, 10,  9,  8;
%e A294317   18, 17, 16, 15, 14, 13, 12, 11, 10, 9;
%e A294317   20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10;
%e A294317   ...
%t A294317 Column[Table[2*n-k, {n, 0, 10}, {k, 0, n}], Center]
%o A294317 (Python)
%o A294317 def f(x):
%o A294317     a=[]
%o A294317     for k in range(x):
%o A294317         for m in range (k+1):
%o A294317             a.append(2*k-m)
%o A294317     return a
%o A294317 print(f(10))
%o A294317 (GAP) A294317 := Flat(List([0..149],n->List([0..n],k->2*n-k))); # _Muniru A Asiru_, Dec 29 2017
%Y A294317 Cf. A001477, A005408, A005843, A287326.
%K A294317 nonn,tabl,easy
%O A294317 0,2
%A A294317 _Kolosov Petro_, Oct 28 2017
%E A294317 Edited by _Wolfdieter Lang_, Dec 08 2017