

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.


3



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
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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



