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
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 ...
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 *)