A390524 Array read by ascending antidiagonals: A(n, k) = k * Fibonacci(n).

0, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 2, 2, 3, 0, 0, 3, 4, 3, 4, 0, 0, 5, 6, 6, 4, 5, 0, 0, 8, 10, 9, 8, 5, 6, 0, 0, 13, 16, 15, 12, 10, 6, 7, 0, 0, 21, 26, 24, 20, 15, 12, 7, 8, 0, 0, 34, 42, 39, 32, 25, 18, 14, 8, 9, 0, 0, 55, 68, 63, 52, 40, 30, 21, 16, 9, 10, 0

Offset

0,9

Links

Table of n, a(n) for n=0..77.

Formula

G.f.: x*y/((1 - x - x^2)*(1 - y)^2).

E.g.f.: 2*exp(x/2+y)*y*sinh(sqrt(5)*x/2)/sqrt(5).

Sum_{k=0..n} A(n, k) = A001924(n-1).

Example

The array begins as:
  0, 0,  0,  0,  0,  0,  0, ...
  0, 1,  2,  3,  4,  5,  6, ...
  0, 1,  2,  3,  4,  5,  6, ...
  0, 2,  4,  6,  8, 10, 12, ...
  0, 3,  6,  9, 12, 15, 18, ...
  0, 5, 10, 15, 20, 25, 30, ...
  ...

Mathematica

A[n_, k_]:=k*Fibonacci[n]; Table[A[n-k, k], {n, 0, 11}, {k, 0, n}]//Flatten

Crossrefs

Cf. A001924, A045925 (main diagonal).

Columns give: A000004 (k=0), A000045 (k=1), A022086 - A022093 (k=3..9), A022345 - A022366 (k=11..32).

Rows give: A000004 (n=0), A001477 (n=1..2), A005843 (n=3), A008585 (n=4), A008587 (n=5), A008590 (n=6).

Sequence in context: A273514 A048866 A262904 * A391449 A397518 A144377

Adjacent sequences: A390521 A390522 A390523 * A390525 A390526 A390527

Keyword

nonn,easy,tabl

Author

Stefano Spezia, Nov 09 2025

Status

approved