A217536 Square array read by antidiagonals, where the top row is the nonnegative integers and the other numbers are the sum of the neighbors in the preceding row.

0, 1, 1, 2, 3, 4, 3, 6, 10, 14, 4, 9, 18, 32, 46, 5, 12, 27, 55, 101, 147, 6, 15, 36, 81, 168, 315, 462, 7, 18, 45, 108, 244, 513, 975, 1437, 8, 21, 54, 135, 324, 736, 1564, 2539, 3976, 9, 24, 63, 162, 405, 973, 2222, 4761, 8737, 12713

Offset

1,4

Comments

Each number in the top row of the array is determined by the pre-defined sequence (in this case, the nonnegative integers). Each number in lower rows is the sum of the numbers vertically or diagonally above it (so, the number at the left end of each row is the sum of two numbers, and all other numbers the sum of three).

Links

Table of n, a(n) for n=1..55.

Formula

T(m+1,n) = sum(T(m,k), |k-n| <= 1) (and T(0,n)=n), m, n >= 0. - M. F. Hasler, Oct 09 2012

Example

The array starts:
0  1  2  3
1  3  6  9
4  10 18 27
14 32 55 81

Crossrefs

Sequence in context: A103634 A255046 A098596 * A333618 A058267 A048259

Adjacent sequences: A217533 A217534 A217535 * A217537 A217538 A217539

Keyword

nonn,tabl

Author

WG Zeist, Oct 06 2012

Status

approved