A047848 Array T read by diagonals; n-th difference of (T(k,n),T(k,n-1),...,T(k,0)) is (k+2)^(n-1), for n=1,2,3,...; k=0,1,2,...

1, 2, 1, 5, 2, 1, 14, 6, 2, 1, 41, 22, 7, 2, 1, 122, 86, 32, 8, 2, 1, 365, 342, 157, 44, 9, 2, 1, 1094, 1366, 782, 260, 58, 10, 2, 1, 3281, 5462, 3907, 1556, 401, 74, 11, 2, 1, 9842, 21846, 19532, 9332, 2802, 586, 92, 12, 2, 1, 29525, 87382

Offset

0,2

Links

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

Formula

T(k, n) = ((k+3)^n+k+1)/(k+2). - Ralf Stephan, Feb 14 2004

Example

Diagonals (each starting on row 1): {1}; {2,1}; {5,2,1}; ...

Crossrefs

Row 1 = (1, 2, 5, 14, 41, ...) = A007051.

Row 2 = (1, 2, 6, 22, 86, ...) = A047849.

Row 3 = (1, 2, 7, 32, 157, ...) = A047850.

Row 4 = (1, 2, 8, 44, 260, ...) = A047851.

Row 5 = (1, 2, 9, 58, 401, ...) = A047852.

Row 6 = (1, 2, 10, 74, 586, ...) = A047853.

Row 7 = (1, 2, 11, 92, 821, ...) = A047854.

Row 8 = (1, 2, 12, 112, 1112, ...) = A047855.

Row 9 = (1, 2, 13, 134, 1465, ...) = A047856.

Sequence in context: A137151 A328082 A048494 * A275431 A281348 A371305

Adjacent sequences: A047845 A047846 A047847 * A047849 A047850 A047851

Keyword

nonn,tabl

Author

Clark Kimberling

Status

approved