A389800 Array read by ascending antidiagonals: A(n, k) = A000045(n)^2 + A000045(n+k)^2.

0, 2, 1, 2, 2, 1, 8, 5, 5, 4, 18, 13, 10, 10, 9, 50, 34, 29, 26, 26, 25, 128, 89, 73, 68, 65, 65, 64, 338, 233, 194, 178, 173, 170, 170, 169, 882, 610, 505, 466, 450, 445, 442, 442, 441, 2312, 1597, 1325, 1220, 1181, 1165, 1160, 1157, 1157, 1156, 6050, 4181, 3466, 3194, 3089, 3050, 3034, 3029, 3026, 3026, 3025

Offset

0,2

Links

Table of n, a(n) for n=0..65.

Formula

G.f.: (-(-1 + y)^2 + x*(-2 + y*(6 + (-3 + y)*y)) + x^2*(2 + y*(-5 + y*(-1 + 2*y))))/((1 + x)*(1 + (-3 + x)*x)*(-1 + 3*y - 3*y^3 + y^4)).

A(n, 1) = A001519(n+1).

A(n, 3) = A126358(n+1).

A(1, n) = A245306(n+1).

Example

The array begins as:
   0,  1,   1,   4,    9,   25,   64, ...
   2,  2,   5,  10,   26,   65,  170, ...
   2,  5,  10,  26,   65,  170,  442, ...
   8, 13,  29,  68,  173,  445, 1160, ...
  18, 34,  73, 178,  450, 1165, 3034, ...
  50, 89, 194, 466, 1181, 3050, 7946, ...
  ...

Mathematica

A[n_, k_]:=Fibonacci[n]^2+Fibonacci[n+k]^2; Table[A[n-k, k], {n, 0, 10}, {k, 0, n}]//Flatten

Crossrefs

Cf. A045702 (sorted without duplicates), A390581 (antidiagonal sums).

Cf. A000045, A001519, A007598 (n=0), A069921 (k=2), A126358, A175395 (k=0), A245306.

Sequence in context: A273138 A181281 A171683 * A249130 A134997 A355691

Adjacent sequences: A389797 A389798 A389799 * A389801 A389802 A389803

Keyword

nonn,easy,tabl

Author

Stefano Spezia, Nov 11 2025

Status

approved