cp's OEIS Frontend

Empirical: a(n) = 2*a(n-1) + 4*a(n-2) + 7*a(n-4) + 8*a(n-5) - a(n-8).

Empirical g.f.: 2*x*(3 + 12*x + 3*x^2 + 11*x^3 + 21*x^4 - 3*x^5 - 3*x^7) / (1 - 2*x - 4*x^2 - 7*x^4 - 8*x^5 + x^8). - Colin Barker, Feb 20 2018

Empirical: a(n) = 2*a(n-1) + 7*a(n-2) + 2*a(n-3) + 13*a(n-4) + 27*a(n-5) + 8*a(n-6) - 4*a(n-7) - 4*a(n-8) - 2*a(n-9) + a(n-10).

Empirical g.f.: 4*x*(2 + 12*x + 8*x^2 + 11*x^3 + 38*x^4 + 10*x^5 - 10*x^6 - 6*x^7 - 4*x^8 + 2*x^9) / (1 - 2*x - 7*x^2 - 2*x^3 - 13*x^4 - 27*x^5 - 8*x^6 + 4*x^7 + 4*x^8 + 2*x^9 - x^10). - Colin Barker, Jun 21 2018

Empirical: a(n) = 3*a(n-1) +6*a(n-2) +a(n-3) +36*a(n-4) +49*a(n-5) +31*a(n-6) +66*a(n-7) +45*a(n-8) +15*a(n-9) -5*a(n-10) -16*a(n-11) -a(n-12) -a(n-13) +a(n-14)

Empirical: a(n) = 3*a(n-1) +9*a(n-2) +4*a(n-3) +58*a(n-4) +117*a(n-5) +100*a(n-6) +160*a(n-7) +169*a(n-8) +74*a(n-9) -12*a(n-10) -67*a(n-11) -26*a(n-12) +6*a(n-13) +3*a(n-14) +3*a(n-15) -a(n-16)

Empirical: a(n) = 4*a(n-1) +7*a(n-2) +4*a(n-3) +102*a(n-4) +156*a(n-5) +223*a(n-6) +518*a(n-7) +545*a(n-8) +578*a(n-9) +532*a(n-10) +306*a(n-11) +173*a(n-12) -124*a(n-13) -147*a(n-14) -50*a(n-15) -14*a(n-16) +22*a(n-17) +a(n-18) +2*a(n-19) -a(n-20)

Empirical: a(n) = (5/6)*n^4 + (35/3)*n^3 - (5/6)*n^2 - (5/3)*n.

Conjectures from Colin Barker, Jun 21 2018: (Start)

G.f.: 10*x*(1 + 5*x - 3*x^2 - x^3) / (1 - x)^5.

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

(End)

Empirical: a(n) = (4/15)*n^5 + (32/3)*n^4 + (44/3)*n^3 - (32/3)*n^2 + (16/15)*n.

Conjectures from Colin Barker, Jun 21 2018: (Start)

G.f.: 16*x*(1 + 10*x - 4*x^2 - 6*x^3 + x^4) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Empirical: a(n) = (13/180)*n^6 + (143/20)*n^5 + (1235/36)*n^4 - (39/4)*n^3 - (377/45)*n^2 + (13/5)*n.

Conjectures from Colin Barker, Jun 21 2018: (Start)

G.f.: 26*x*(1 + 19*x + 2*x^2 - 28*x^3 + 7*x^4 + x^5) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Empirical: a(n) = (1/60)*n^7 + (77/20)*n^6 + (2527/60)*n^5 + (119/4)*n^4 - (644/15)*n^3 + (42/5)*n^2 + (4/5)*n.

Conjectures from Colin Barker, Jun 21 2018: (Start)

G.f.: 42*x*(1 + 34*x + 35*x^2 - 96*x^3 + 15*x^4 + 14*x^5 - x^6) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)