cp's OEIS Frontend

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

G.f: 4*x -x^2*(-16-20*x-29*x^2-4*x^3+13*x^4+9*x^5) / ( (x^3+2*x^2+x-1)*(x^3-x^2-1) ). - R. J. Mathar, Aug 10 2017

Empirical: 31*a(n) = 114*A002478(n) +133*A002478(n-1) +55*A002478(n) +10*A077961(n) +32*A077961(n-1) -24*A077961(n-2) for n>1. - R. J. Mathar, Nov 09 2018

Empirical: a(n) = a(n-1) + 9*a(n-3) + 2*a(n-4) + 2*a(n-5) - 12*a(n-6) - 8*a(n-7) + 8*a(n-9) for n>11.

Empirical g.f.: x*(6 + 30*x + 54*x^2 + 117*x^3 + 27*x^4 - 36*x^5 - 203*x^6 - 134*x^7 + 28*x^8 + 120*x^9 + 16*x^10) / (1 - x - 9*x^3 - 2*x^4 - 2*x^5 + 12*x^6 + 8*x^7 - 8*x^9). - Colin Barker, Mar 05 2018

Empirical: a(n) = 9*n^3 + 9*n - 9.

Conjectures from Colin Barker, Jun 19 2018: (Start)

G.f.: 9*x*(1 + 5*x - x^2 + x^3) / (1 - x)^4.

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

(End)

Empirical: a(n) = (13/4)*n^4 + (13/2)*n^3 + (117/4)*n^2 - 26*n.

Conjectures from Colin Barker, Jun 19 2018: (Start)

G.f.: 13*x*(1 + 8*x - 7*x^2 + 4*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) = (19/4)*n^4 + (95/2)*n^3 - (57/4)*n^2 - 19*n.

Conjectures from Colin Barker, Jun 20 2018: (Start)

G.f.: 19*x*(1 + 14*x - 7*x^2 - 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) = 35*n^4 + 42*n^3 + 7*n^2 - 84*n + 28.

Conjectures from Colin Barker, Jun 20 2018: (Start)

G.f.: 28*x*(1 + 23*x + 6*x^2 - x^3 + x^4) / (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) = a(n-1) + 13*a(n-3) + 3*a(n-4) + 3*a(n-5) - 27*a(n-6) - 18*a(n-7) + 27*a(n-9) for n>11.

Empirical g.f.: x*(8 + 56*x + 104*x^2 + 331*x^3 + 153*x^4 - 60*x^5 - 819*x^6 - 828*x^7 - 54*x^8 + 837*x^9 + 324*x^10) / ((1 - x - 13*x^3 - 3*x^4 - 3*x^5 + 27*x^6 + 18*x^7 - 27*x^9)). - Colin Barker, Jun 20 2018

Empirical: a(n) = a(n-1) + 17*a(n-3) + 4*a(n-4) + 4*a(n-5) - 48*a(n-6) - 32*a(n-7) + 64*a(n-9) for n>11.

Empirical g.f.: x*(10 + 90*x + 170*x^2 + 721*x^3 + 544*x^4 - 20*x^5 - 2284*x^6 - 3216*x^7 - 800*x^8 + 3392*x^9 + 2304*x^10) / ((1 - 2*x - 8*x^3)*(1 + x + 2*x^2 - 5*x^3 - 6*x^4 + 8*x^6)). - Colin Barker, Jun 20 2018

Empirical: a(n) = a(n-1) + 21*a(n-3) + 5*a(n-4) + 5*a(n-5) - 75*a(n-6) - 50*a(n-7) + 125*a(n-9) for n>11.

Empirical g.f.: x*(12 + 132*x + 252*x^2 + 1341*x^3 + 1440*x^4 + 180*x^5 - 5150*x^6 - 9425*x^7 - 3500*x^8 + 10125*x^9 + 10000*x^10) / (1 - x - 21*x^3 - 5*x^4 - 5*x^5 + 75*x^6 + 50*x^7 - 125*x^9). - Colin Barker, Jun 21 2018