A219795 Sum of the absolute values of the antidiagonals of the triangle A135929(n) companion. See the comment.

2, 2, 2, 2, 3, 3, 5, 7, 10, 11, 16, 23, 33, 44, 58, 81, 114, 158, 212, 293, 407, 565, 777, 1064, 1471, 2036, 2813, 3863, 5334, 7370, 10183, 14046, 19356, 26726, 36909, 50955, 70251, 96977, 133886, 184841, 255092

Offset

0,1

Comments

The companion to A135929(n) is the triangle

2;

2, 0;

2, 0, 1;

2, 0, -1, 0;

2, 0, -3, 0, -1;

2, 0, -5, 0, 0, 0;

2, 0, -7, 0, 3, 0, 1;

2, 0, -9, 0, 8, 0, 1, 0;

(A192011(n) beginning with 2 instead of -1).

Consider a(1),a(5),a(10),a(14), that is, a(A193910(n) -1).

a(1)+a(4)-a(5) = 2, a(5)+a(8)-a(9) = 2, a(10)+a(13)-a(14) = 2, a(14)+a(17)-a(18) = 4, a(19)+a(22)-a(23) = 6, a(23)+a(26)-a(27) = 14, yields 2,2,2,4,6,14,24,60,... = 2*A047749(n) or 2, followed with A116637(n+1).

Links

Table of n, a(n) for n=0..40.

Formula

a(n) = sum abs ( [k=0..floor(n/2)] A192011(n-k,k) ), a(0)=2.

Example

a(0)=2, a(1)=2, a(2)=2+0, a(3)=2+0, a(4)=2+0+1, a(5)=2+0+1.

Maple

A219795 := proc(n)
    if n=0 then
        2;
    else
        add(abs(A192011(n-k, k)), k=0..floor(n/2)) ;
    end if;
end proc: # R. J. Mathar, Jan 06 2013

Crossrefs

Sequence in context: A285798 A321346 A291444 * A082602 A216644 A187758

Adjacent sequences: A219792 A219793 A219794 * A219796 A219797 A219798

Keyword

nonn

Author

Paul Curtz, Nov 28 2012

Extensions

a(24)-a(40) from Jean-Francois Alcover, Nov 28 2012

Status

approved