A222405 Triangle read by rows: left and right edges are A002061 (1,3,7,13,21,...), interior entries are filled in using the Pascal triangle rule.

1, 3, 3, 7, 6, 7, 13, 13, 13, 13, 21, 26, 26, 26, 21, 31, 47, 52, 52, 47, 31, 43, 78, 99, 104, 99, 78, 43, 57, 121, 177, 203, 203, 177, 121, 57, 73, 178, 298, 380, 406, 380, 298, 178, 73, 91, 251, 476, 678, 786, 786, 678, 476, 251, 91, 111, 342, 727, 1154, 1464, 1572, 1464, 1154, 727, 342, 111

Offset: 0

Author

N. J. A. Sloane, Feb 18 2013

Keywords

• nonn
• tabl

Examples

			Triangle begins:
1
3, 3
7, 6, 7
13, 13, 13, 13
21, 26, 26, 26, 21
31, 47, 52, 52, 47, 31
43, 78, 99, 104, 99, 78, 43
57, 121, 177, 203, 203, 177, 121, 57
73, 178, 298, 380, 406, 380, 298, 178, 73
...
		

Crossrefs

Cf. A007318, A002061, A222403, A222404.

Row sums are A027178.

Programs

Maple

d:=[seq(n*(n+1)+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^2+n+1; t[n_, 0] := n^2+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 14 2014 *)