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

0,2

Links

Table of n, a(n) for n=0..63.

Example

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.

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:

Crossrefs

Rows are the partial sums of the rows of A245557.

Main "spine" of triangle is A090381.

Row sums are A005915.

Sequence in context: A199959 A084892 A344475 * A256318 A018835 A055166

Adjacent sequences: A245553 A245554 A245555 * A245557 A245558 A245559

Keyword

nonn,tabf

Author

N. J. A. Sloane, Aug 04 2014

Status

approved