A222404 Triangle read by rows: left and right edges are A002378, interior entries are filled in using the Pascal triangle rule.

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

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..M-1, 0..M-1);
for n from 0 to M-1 do T[n, 0]:=d[n+1]; T[n, n]:=d[n+1]; od:
for n from 2 to M-1 do
for i from 1 to n-1 do T[n, i]:=T[n-1, i-1]+T[n-1, i]; od: od:
lprint("triangle:");
for n from 0 to M-1 do lprint(seq(T[n, i], i=0..n)); od:
lprint("row sums:");
lprint([seq( add(T[i, j], j=0..i), i=0..M-1)]);
end;
f(d);

Mathematica

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

Crossrefs

Cf. A007318, A002378, A222403, A222405.

Row sums are 4*A000295.

Sequence in context: A371824 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