

A157458


Triangle, read by rows, double tent function: T(n,k) = min(1 + 2*k, 1 + 2*(nk), n).


2



0, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 3, 4, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 6, 5, 3, 1, 1, 3, 5, 7, 7, 5, 3, 1, 1, 3, 5, 7, 8, 7, 5, 3, 1, 1, 3, 5, 7, 9, 9, 7, 5, 3, 1, 1, 3, 5, 7, 9, 10, 9, 7, 5, 3, 1, 1, 3, 5, 7, 9, 11, 11, 9, 7, 5, 3, 1, 1, 3, 5, 7, 9, 11, 12, 11, 9, 7, 5, 3, 1, 1, 3, 5, 7, 9, 11, 13, 13, 11, 9, 7, 5, 3, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,5


COMMENTS

The general form of this, and related triangular sequences, takes the form A(n, k, m) = (m*(nk) + 1)*A(n1, k1, m) + (m*k + 1)*A(n1, k, m) + m*f(n, k)* A(n2, k1, m), where f(n,k) is a polynomial in n and k.
Row sums are: 0, 2, 4, 8, 12, 18, 24, 32, 40, 50, 60, ... = A007590(n+1).  N. J. A. Sloane, Aug 27 2009


LINKS

Nathaniel Johnston, Table of n, a(n) for n = 0..10000


FORMULA

T(n, k) = min(1 + 2*k, 1 + 2*(n  k), n).
From YuSheng Chang, May 19 2020: (Start)
O.g.f.: F(z,v) = (1+v)*z/((1v*z1)*(1z)*(1v*z^2)).
T(n,k) = [v^k] (1+v)*(2*v^(n+1)+2((sqrt(v)1)^2 * (1)^n + (sqrt(v)+1)^2) * v^((1/2)*n))/(2*(v1)^2). (End)


EXAMPLE

Triangle begins as:
0;
1, 1;
1, 2, 1;
1, 3, 3, 1;
1, 3, 4, 3, 1;
1, 3, 5, 5, 3, 1;
1, 3, 5, 6, 5, 3, 1;
1, 3, 5, 7, 7, 5, 3, 1;
1, 3, 5, 7, 8, 7, 5, 3, 1;
1, 3, 5, 7, 9, 9, 7, 5, 3, 1;
1, 3, 5, 7, 9, 10, 9, 7, 5, 3, 1;


MAPLE

T := proc(m, n) return min(1+2*m, 1+2*(nm), n): end: seq(seq(T(m, n), m=0..n), n=0..14); # Nathaniel Johnston, Apr 29 2011


MATHEMATICA

T[n_, k_]:= Min[1+2*k, 1+2*(nk), n]; Table[T[n, k], {n, 0, 14}, {k, 0, n}]//Flatten


CROSSREFS

Cf. A003983, A157457.
Sequence in context: A155582 A169946 A160832 * A174447 A174374 A242641
Adjacent sequences: A157455 A157456 A157457 * A157459 A157460 A157461


KEYWORD

nonn,tabl,easy


AUTHOR

Roger L. Bagula, Mar 01 2009


EXTENSIONS

Edited by N. J. A. Sloane, Aug 27 2009
More terms from and partially edited by G. C. Greubel, May 21 2020


STATUS

approved



