A245556 Irregular triangle read by rows: T(n,k) (n>=0, 0 <= k <= 2n) = number of triples (u,v,w) with entries in the range 0 to n which have some pair adding up to k.

1, 4, 6, 4, 7, 12, 19, 12, 7, 10, 18, 28, 36, 28, 18, 10, 13, 24, 37, 48, 61, 48, 37, 24, 13, 16, 30, 46, 60, 76, 90, 76, 60, 46, 30, 16, 19, 36, 55, 72, 91, 108, 127, 108, 91, 72, 55, 36, 19, 22, 42, 64, 84, 106, 126, 148, 168, 148, 126, 106, 84, 64, 42, 22

Offset: 0

Author

N. J. A. Sloane, Aug 04 2014

Keywords

• nonn
• tabf

Examples

			Triangle begins:
[1]
[4, 6, 4]
[7, 12, 19, 12, 7]
[10, 18, 28, 36, 28, 18, 10]
[13, 24, 37, 48, 61, 48, 37, 24, 13]
[16, 30, 46, 60, 76, 90, 76, 60, 46, 30, 16]
[19, 36, 55, 72, 91, 108, 127, 108, 91, 72, 55, 36, 19]
[22, 42, 64, 84, 106, 126, 148, 168, 148, 126, 106, 84, 64, 42, 22]
...
See A245557 for specific examples; also the Example section of A090381 for some of the T(10,10)= 331 triples with n=k=10.
		

Crossrefs

Rows are the partial sums of the rows of A245557.

Main "spine" of triangle is A090381.

Row sums are A005915.

Programs

Maple

with(LinearAlgebra);
M:=10; A:=Array(0..M,0..2*M); B:=Array(0..M,0..2*M);
for n from 0 to M do
for i from 0 to n do for j from 0 to n do for k from 0 to n do
  s1:={i+j,i+k,j+k}; s1:=convert(s1,list); m1:=max(i,j,k);
    for r1 from 1 to nops(s1) do
       s:=s1[r1]; A[n,s] := A[n,s]+1;
       if (m1=n) then B[n,s] := B[n,s]+1; fi;
                              od:
od: od: od: od:
lprint("A245556");
for i from 0 to M do lprint([seq(A[i,j],j=0..2*i)]); od:
lprint("A245557");
for i from 0 to M do lprint([seq(B[i,j],j=0..2*i)]); od: