cp's OEIS Frontend

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2) +a(n-3)

k=2: a(n) = 3*a(n-1) +3*a(n-2) +3*a(n-3)

k=3: a(n) = 6*a(n-1) +11*a(n-2) +26*a(n-3) -5*a(n-4) -5*a(n-6)

k=4: a(n) = 12*a(n-1) +45*a(n-2) +180*a(n-3) -27*a(n-4) -81*a(n-6)

Columns k=1..z+1 for an underlying 0..z array: a(n) = sum(i=1..2z+1){(2^k-1)*a(n-i)} checked for z=1..3.

Empirical: a(n) = 3*a(n-1) + a(n-2) + a(n-3).

Empirical g.f.: x*(3 + x^2) / (1 - 3*x - x^2 - x^3). - Colin Barker, Aug 05 2018

Empirical: a(n) = 5*a(n-1) + 11*a(n-2) + a(n-3).

Empirical g.f.: x*(5 + 8*x + x^2) / (1 - 5*x - 11*x^2 - x^3). - Colin Barker, Aug 05 2018

Empirical: a(n) = 9*a(n-1) + 42*a(n-2) + 34*a(n-3) - 21*a(n-4) - 11*a(n-5) - 4*a(n-6).

Empirical g.f.: x*(9 + 36*x + 34*x^2 - 12*x^3 - 11*x^4 - 8*x^5) / (1 - 9*x - 42*x^2 - 34*x^3 + 21*x^4 + 11*x^5 + 4*x^6). - Colin Barker, Aug 05 2018

Empirical: a(n) = 17*a(n-1) +168*a(n-2) +464*a(n-3) +442*a(n-4) +30*a(n-5) -88*a(n-6) -9*a(n-8) +a(n-9)

Empirical: a(n) = 31*a(n-1) +737*a(n-2) +4637*a(n-3) +10078*a(n-4) +3446*a(n-5) -14110*a(n-6) -4246*a(n-7) -1045*a(n-8) +11211*a(n-9) -13907*a(n-10) +5385*a(n-11) -2232*a(n-12) +16*a(n-13) for n>15

Empirical: a(n) = 3*a(n-1) + a(n-2) + 5*a(n-3) + a(n-4) + a(n-5) - a(n-6) - a(n-7).

Empirical g.f.: x*(1 + 6*x + 5*x^2 + 4*x^3 - x^4 - 2*x^5 - x^6) / ((1 + x^2)*(1 - 3*x - 2*x^2 - 2*x^3 + x^4 + x^5)). - Colin Barker, Aug 05 2018

Empirical: a(n) = 5*a(n-1) +8*a(n-2) +46*a(n-3) +39*a(n-4) +69*a(n-5) -10*a(n-6) -38*a(n-7) -68*a(n-8) -40*a(n-9) +50*a(n-10) +18*a(n-11) -13*a(n-12) -7*a(n-13) +4*a(n-14) +2*a(n-15) -a(n-16) +a(n-17)