A116637 -id:A116637 - cp's OEIS frontend

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

Paul Curtz, Nov 28 2012

nonn

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).

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

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

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

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

cp's OEIS Frontend

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

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