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A275175
a(n) = (2 * a(n-3) + a(n-1) * a(n-5)) / a(n-6), a(0) = a(1) = ... = a(5) = 1.
3
1, 1, 1, 1, 1, 1, 3, 5, 7, 13, 23, 83, 147, 215, 423, 771, 2801, 4971, 7281, 14351, 26181, 95133, 168845, 247317, 487493, 889373, 3231703, 5735737, 8401475, 16560393, 30212491, 109782751, 194846191, 285402811, 562565851, 1026335311, 3729381813, 6619034735, 9695294077, 19110678523
OFFSET
0,7
COMMENTS
Inspired by A048736.
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,35,0,0,0,0,-35,0,0,0,0,1).
FORMULA
G.f.: (1 +x +x^2 +x^3 +x^4 -34*x^5 -32*x^6 -30*x^7 -28*x^8 -22*x^9 +23*x^10 +13*x^11 +7*x^12 +5*x^13 +3*x^14) / ((1 -x)*(1 +x +x^2 +x^3 +x^4)*(1 -34*x^5 +x^10)). - Colin Barker, Jul 19 2016
a(n) = 35*a(n-5) - 35*a(n-10) + a(n-15). - G. C. Greubel, Jul 20 2016
MATHEMATICA
RecurrenceTable[{a[n] == (2 a[n - 3] + a[n - 1] a[n - 5])/a[n - 6], a[1] == 1, a[2] == 1, a[3] == 1, a[4] == 1, a[5] == 1, a[6] == 1}, a, {n, 40}] (* Michael De Vlieger, Jul 19 2016 *)
PROG
(Ruby)
def A(k, l, n)
a = Array.new(k * 2, 1)
ary = [1]
while ary.size < n + 1
break if (a[1] * a[-1] + a[k] * l) % a[0] > 0
a = *a[1..-1], (a[1] * a[-1] + a[k] * l) / a[0]
ary << a[0]
end
ary
end
def A275175(n)
A(3, 2, n)
end
(PARI) Vec((1 +x +x^2 +x^3 +x^4 -34*x^5 -32*x^6 -30*x^7 -28*x^8 -22*x^9 +23*x^10 +13*x^11 +7*x^12 +5*x^13 +3*x^14) / ((1 -x)*(1 +x +x^2 +x^3 +x^4)*(1 -34*x^5 +x^10)) + O(x^50)) \\ Colin Barker, Jul 19 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jul 19 2016
STATUS
approved