A340459 a(n) is the sum of the numbers adjacent to n in a triangle in which the nonnegative integers are placed from top to bottom and from left to right.

3, 9, 10, 18, 26, 23, 31, 44, 50, 40, 48, 68, 74, 80, 61, 69, 98, 104, 110, 116, 86, 94, 134, 140, 146, 152, 158, 115, 123, 176, 182, 188, 194, 200, 206, 148, 156, 224, 230, 236, 242, 248, 254, 260, 185, 193, 278, 284, 290, 296, 302, 308, 314, 320, 226, 234, 338

Offset: 0

Author

Leonardo Sznajder, Jan 10 2021

Keywords

• nonn

Comments

The triangle of nonnegative integers begins:

0

1 2

3 4 5

6 7 8 9

...

Examples

			For n=4:
- the numbers adjacent to 4 are 1, 2, 3, 5, 7 and 8,
- so a(4) = 1 + 2 + 3 + 5 + 7 + 8 = 26.
		

Crossrefs

Cf. A214177.

Programs

Mathematica

T[i_,j_]:=Binomial[i+1,2]+j; a[i_,j_]:=If[j-1>=0,T[i,j-1],0]+If[i-1>=0&&j-1>=0, T[i-1,j-1],0]+If[i-1>=0&&j<=i-1,T[i-1,j],0]+If[j+1<=i,T[i,j+1],0]+T[i+1,j]+T[i+1,j+1]; Flatten[Table[a[i,j],{i,0,12},{j,0,i}]] (* Stefano Spezia, Jan 28 2021 *)

Extensions

More terms from Stefano Spezia, Jan 28 2021