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A275174 a(n) = (a(n-4) + a(n-1) * a(n-7)) / a(n-8), a(0) = a(1) = ... = a(7) = 1. 2
1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 7, 10, 14, 33, 53, 74, 96, 141, 209, 300, 714, 1151, 1611, 2094, 3083, 4578, 6579, 15665, 25257, 35355, 45959, 67673, 100497, 144431, 343906, 554491, 776186, 1008991, 1485711, 2206346, 3170896, 7550257, 12173533, 17040724 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

Inspired by A048736.

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,23,0,0,0,0,0,0,-23,0,0,0,0,0,0,1).

FORMULA

G.f.: (1 +x +x^2 +x^3 +x^4 +x^5 +x^6 -22*x^7 -21*x^8 -20*x^9 -19*x^10 -18*x^11 -16*x^12 -13*x^13 +14*x^14 +10*x^15 +7*x^16 +5*x^17 +4*x^18 +3*x^19 +2*x^20) / ((1 -x)*(1 +x +x^2 +x^3 +x^4 +x^5 +x^6)*(1 -22*x^7 +x^14)). - Colin Barker, Jul 19 2016

a(n) = 23*a(n-7) - 23*a(n-14) + a(n-21).

MATHEMATICA

RecurrenceTable[{a[n] == (a[n - 4] + a[n - 1] a[n - 7])/a[n - 8], a[1] == 1, a[2] == 1, a[3] == 1, a[4] == 1, a[5] == 1, a[6] == 1, a[7] == 1, a[8] == 1}, a, {n, 42}] (* 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 A275174(n)

  A(4, 1, n)

end

(PARI) Vec((1 +x +x^2 +x^3 +x^4 +x^5 +x^6 -22*x^7 -21*x^8 -20*x^9 -19*x^10 -18*x^11 -16*x^12 -13*x^13 +14*x^14 +10*x^15 +7*x^16 +5*x^17 +4*x^18 +3*x^19 +2*x^20) / ((1 -x)*(1 +x +x^2 +x^3 +x^4 +x^5 +x^6)*(1 -22*x^7 +x^14)) + O(x^20)) \\ Colin Barker, Jul 19 2016

CROSSREFS

Cf. A101879, A048736, A275173.

Sequence in context: A206739 A107586 A206737 * A282582 A282502 A212463

Adjacent sequences:  A275171 A275172 A275173 * A275175 A275176 A275177

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Jul 19 2016

STATUS

approved

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Last modified October 19 22:00 EDT 2018. Contains 316378 sequences. (Running on oeis4.)