A367293 Main diagonal of the extended Wythoff array (A287870).

0, 3, 6, 15, 32, 60, 118, 212, 398, 733, 1275, 2296, 4092, 6998, 12310, 20905, 36409, 63092, 106266, 182888, 306865, 525175, 896119, 1496319, 2542488, 4310250, 7170549, 12116421, 20119010, 33899511, 57028870, 94452959, 158530985, 265735987, 439197324, 734794015, 1213079508, 2026049861

Offset: 0

Author

Thomas Scheuerle, Nov 12 2023

Keywords

• nonn

Crossrefs

Cf. A000045, A000201, A001468, A020941, A099920, A287870.

Programs

PARI

a(n)  = (1 + n + sqrtint(5*(n+1)^2))\2*fibonacci(n) + n*fibonacci(n-1)

Formula

a(n) = A287870(n+1, n+1).

a(n) = n*Fibonacci(n-1) + Fibonacci(n)*floor(((1 + sqrt(5))*(1 + n))/2), for n > 0.

a(n) = A099920(n-1) + A000045(n)*A000201(n+1) for n > 0.

a(n) = A035513(n+1, n-1) for n >= 2.