A135686 a(n) = a(n-1) + A000045(n)*a(n-2), a(1) = 1, a(2) = 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

G. C. Greubel, Table of n, a(n) for n = 1..100

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

Adjacent sequences: A135683 A135684 A135685 * A135687 A135688 A135689

Keyword

nonn,less

Author

Roger L. Bagula, Feb 18 2008

Extensions

Corrected and edited by Joerg Arndt, Oct 26 2016

Status

approved