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

0,2

Links

Table of n, a(n) for n=0..37.

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.

Prog

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

Crossrefs

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

Sequence in context: A006961 A316219 A034740 * A323936 A305839 A322110

Adjacent sequences: A367290 A367291 A367292 * A367294 A367295 A367296

Keyword

nonn

Author

Thomas Scheuerle, Nov 12 2023

Status

approved