cp's OEIS Frontend

Empirical: a(n) = 4*a(n-1) + 4*a(n-2) for n>3.

Conjectures from Colin Barker, Jan 31 2019: (Start)

G.f.: 4*x*(1 + 8*x + 4*x^2) / (1 - 4*x - 4*x^2).

a(n) = 2*((2-2*sqrt(2))^n + (2*(1+sqrt(2)))^n) for n>1.

(End)

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

Conjectures from Colin Barker, Jan 31 2019: (Start)

G.f.: 8*x*(1 + 15*x + 7*x^2 + x^3) / ((1 + x)*(1 - 4*x - x^2)).

a(n) = 8*(2*(-1)^n - (2*((2-sqrt(5))^n - (2+sqrt(5))^n))/sqrt(5)) for n>1.

(End)

Empirical: a(n) = 3*a(n-1) + 10*a(n-2) + 4*a(n-3) - 4*a(n-4) for n>6.

Empirical g.f.: 16*x*(1 + 24*x - 15*x^2 - 98*x^3 - 52*x^4 + 40*x^5) / (1 - 3*x - 10*x^2 - 4*x^3 + 4*x^4). - Colin Barker, Jan 31 2019

Empirical: a(n) = 3*a(n-1) + 18*a(n-2) + 11*a(n-3) - 23*a(n-4) - 4*a(n-5) for n>7.

Empirical g.f.: 16*x*(2 + 75*x - 103*x^2 - 891*x^3 - 647*x^4 + 1172*x^5 + 144*x^6) / (1 - 3*x - 18*x^2 - 11*x^3 + 23*x^4 + 4*x^5). - Colin Barker, Jan 31 2019

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

Empirical g.f.: x*(5 + 21*x - 18*x^2 + 51*x^3 - 20*x^4) / (1 - 3*x + 2*x^2 - x^3). - Colin Barker, Feb 01 2019

Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 10*a(n-3) - 6*a(n-4) + a(n-5) for n>9.

Empirical g.f.: 2*x*(7 + 73*x - 277*x^2 + 446*x^3 - 798*x^4 + 969*x^5 - 1132*x^6 + 768*x^7 - 128*x^8) / ((1 - x)*(1 - 4*x + 5*x^2 - 5*x^3 + x^4)). - Colin Barker, Feb 01 2019

Empirical: a(n) = 8*a(n-1) -27*a(n-2) +56*a(n-3) -75*a(n-4) +61*a(n-5) -28*a(n-6) +7*a(n-7) -a(n-8) for n>12

Empirical: a(n) = 13*a(n-1) -77*a(n-2) +286*a(n-3) -736*a(n-4) +1351*a(n-5) -1787*a(n-6) +1716*a(n-7) -1217*a(n-8) +652*a(n-9) -265*a(n-10) +78*a(n-11) -14*a(n-12) +a(n-13) for n>18

Empirical: a(n) = 21*a(n-1) -209*a(n-2) +1330*a(n-3) -6059*a(n-4) +20839*a(n-5) -55739*a(n-6) +118287*a(n-7) -202495*a(n-8) +284119*a(n-9) -331806*a(n-10) +326718*a(n-11) -273224*a(n-12) +193798*a(n-13) -115270*a(n-14) +56258*a(n-15) -21837*a(n-16) +6481*a(n-17) -1404*a(n-18) +210*a(n-19) -20*a(n-20) +a(n-21) for n>27