login
A135686
a(n) = a(n-1) + A000045(n)*a(n-2), a(1) = 1, a(2) = 1.
1
1, 1, 3, 6, 21, 69, 342, 1791, 13419, 111924, 1306215, 17423271, 321771366, 6890344533, 203170877793, 7003940931864, 331467832767285, 18429651200703861, 1404296660000722446, 126080887032762342111, 15497512127400670236027, 2248516102364654511363948
OFFSET
1,3
LINKS
FORMULA
a(n) = a(n-1) + A000045(n)*a(n-1), with a(1) = 1, a(2) = 1.
MAPLE
a:= proc(n) option remember; `if`(n<2, n,
a(n-2)*(<<0|1>, <1|1>>^n)[1, 2]+a(n-1))
end:
seq(a(n), n=1..25); # Alois P. Heinz, Oct 26 2016
MATHEMATICA
RecurrenceTable[{a[1]==1, a[2]==1, a[n]==a[n-1]+Fibonacci[n+1]a[n-2]}, a, {n, 25}] (* Harvey P. Dale, Feb 07 2012 *)
PROG
(Sage)
@CachedFunction
def a(n): # A135686
if (n<3): return 1
else: return a(n-1) + fibonacci(n)*a(n-2)
[a(n) for n in (1..40)] # G. C. Greubel, Nov 25 2021
CROSSREFS
Cf. A000045.
Sequence in context: A084567 A294527 A261582 * A218244 A151961 A025229
KEYWORD
nonn,less
AUTHOR
Roger L. Bagula, Feb 18 2008
EXTENSIONS
Corrected and edited by Joerg Arndt, Oct 26 2016
STATUS
approved