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A135686
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a(n) = a(n-1) + A000045(n)*a(n-2), a(1) = 1, a(2) = 1.
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1
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1, 1, 3, 6, 21, 69, 342, 1791, 13419, 111924, 1306215, 17423271, 321771366, 6890344533, 203170877793, 7003940931864, 331467832767285, 18429651200703861, 1404296660000722446, 126080887032762342111, 15497512127400670236027, 2248516102364654511363948
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listen;
history;
text;
internal format)
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OFFSET
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1,3
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 1..100
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FORMULA
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a(n) = a(n-1) + A000045(n)*a(n-1), with a(1) = 1, a(2) = 1.
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A000045.
Sequence in context: A084567 A294527 A261582 * A218244 A151961 A025229
Adjacent sequences: A135683 A135684 A135685 * A135687 A135688 A135689
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KEYWORD
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nonn,less
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AUTHOR
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Roger L. Bagula, Feb 18 2008
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EXTENSIONS
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Corrected and edited by Joerg Arndt, Oct 26 2016
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STATUS
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approved
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