1,8

Rows 2,4,6,... give A088459.

Diagonal sums are in A088518 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 04 2009]

Row sums are in A001405 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 04 2009]

Subtriangle (1<=k<=n) of triangle T(n,k), 0<=k<=n, read by rows, given by A101455 DELTA A056594 := [0,1,0,-1,0,1,0,-1,0,1,0,-1,0,...] DELTA [1,0,-1,0,1,0,-1,0,1,0,-1,0,1,...] where DELTA is the operator defined in A084938 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 03 2009]

Paul Barry, On Integer-Sequence-Based Constructions of Generalized Pascal Triangles, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.4.

a(n, k)=binomial(floor(n'), floor(k'))*binomial(ceil(n'), ceil(k')), where n'=(n-1)/2, k'=(k-1)/2. G.f.=2u/[uv+sqrt(xyuv)]-1, where x=1+z+tz, y=1+z-tz, u=1-z+tz, v=1-z-tz.

Triangle T(n,k), 0<=k<=n, given by A101455 DELTA A056594 begins : 1 ; 0,1 ; 0,1,1 ; 0,1,1,1 ; 0,1,2,2,1 ; 0,1,2,4,2,1 ; 0,1,3,6,6,3,1 ; 0,1,3,9,9,9,3,1 ; ... [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 03 2009]

Triangle begins:

1;

1,1;

1,1,1;

1,2,2,1;

1,2,4,2,1;

1,3,6,6,3,1;

1,3,9,9,9,3,1;

1,4,12,18,18,12,4,1;

1,4,16,24,36,24,16,4,1;

1,5,20,40,60,60,40,20,5,1;

1,5,25,50,100,100,100,50,25,5,1;

1,6,30,75,150,200,200,150,75,30,6,1;

1,6,36,90,225,300,400,300,225,90,36,6,1;

1,7,42,126,315,525,700,700,525,315,126,42,7,1;

1,7,49,147,441,735,1225,1225,1225,735,441,147,49,7,1;

1,8,56,196,588,1176,1960,2450,2450,1960,1176,588,196,56,8,1.

a(6,2)=3 because we have UUUDDDUUUDDD, UUUUDDUUDDDD, UUUUUDUDDDDD, where

U=(1,1), D=(1,-1).

Cf. A088459.

Column 2 is A008619, column 3 is A002620, column 4 is A028724, column 5 is A028723 and column 6 is A028725.

Adjacent sequences: A088852 A088853 A088854 this_sequence A088856 A088857 A088858

Sequence in context: A120423 A113137 A075402 this_sequence A034851 A122085 A066287

nonn

Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 24 2003