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
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jul 19 2016
STATUS
approved