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A367293
Main diagonal of the extended Wythoff array (A287870).
0
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
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
KEYWORD
nonn
AUTHOR
Thomas Scheuerle, Nov 12 2023
STATUS
approved