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

0,1

Comments

The triangle of nonnegative integers begins:

0

1 2

3 4 5

6 7 8 9

...

Links

Table of n, a(n) for n=0..56.

Example

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.

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 *)

Crossrefs

Cf. A214177.

Sequence in context: A030794 A134073 A088005 * A125237 A085459 A092169

Adjacent sequences: A340456 A340457 A340458 * A340460 A340461 A340462

Keyword

nonn

Author

Leonardo Sznajder, Jan 10 2021

Extensions

More terms from Stefano Spezia, Jan 28 2021

Status

approved