

A222404


Triangle read by rows: left and right edges are A002378, interior entries are filled in using the Pascal triangle rule.


3



0, 2, 2, 6, 4, 6, 12, 10, 10, 12, 20, 22, 20, 22, 20, 30, 42, 42, 42, 42, 30, 42, 72, 84, 84, 84, 72, 42, 56, 114, 156, 168, 168, 156, 114, 56, 72, 170, 270, 324, 336, 324, 270, 170, 72, 90, 242, 440, 594, 660, 660, 594, 440, 242, 90, 110, 332, 682, 1034, 1254, 1320, 1254, 1034, 682, 332, 110
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OFFSET

0,2


LINKS

Table of n, a(n) for n=0..65.


EXAMPLE

Triangle begins:
0
2, 2
6, 4, 6
12, 10, 10, 12
20, 22, 20, 22, 20
30, 42, 42, 42, 42, 30
42, 72, 84, 84, 84, 72, 42
56, 114, 156, 168, 168, 156, 114, 56
...


MAPLE

d:=[seq(n*(n+1), n=0..14)];
f:=proc(d) local T, M, n, i;
M:=nops(d);
T:=Array(0..M1, 0..M1);
for n from 0 to M1 do T[n, 0]:=d[n+1]; T[n, n]:=d[n+1]; od:
for n from 2 to M1 do
for i from 1 to n1 do T[n, i]:=T[n1, i1]+T[n1, i]; od: od:
lprint("triangle:");
for n from 0 to M1 do lprint(seq(T[n, i], i=0..n)); od:
lprint("row sums:");
lprint([seq( add(T[i, j], j=0..i), i=0..M1)]);
end;
f(d);


MATHEMATICA

t[n_, n_] := n*(n+1); t[n_, 0] := n*(n+1); t[n_, k_] := t[n, k] = t[n1, k1] + t[n1, k]; Table[t[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* JeanFrançois Alcover, Jan 20 2014 *)


CROSSREFS

Cf. A007318, A002378, A222403, A222405.
Row sums are 4*A000295.
Sequence in context: A036500 A077080 A273012 * A081111 A092686 A249796
Adjacent sequences: A222401 A222402 A222403 * A222405 A222406 A222407


KEYWORD

nonn,tabl


AUTHOR

N. J. A. Sloane, Feb 18 2013


STATUS

approved



