cp's OEIS Frontend

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

Conjecture: a(n) = 1+2*floor((2*n^2+2*n)/3). - Clark Kimberling, Apr 12 2012

Empirical g.f.: x*(3 + 3*x + 2*x^2 - x^3 + x^4) / ((1 - x)^3*(1 + x + x^2)). - Colin Barker, Mar 03 2018

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

Conjectures from Colin Barker, Mar 03 2018: (Start)

G.f.: x*(7 + 10*x + 2*x^2 + 4*x^3 - x^4) / ((1 - x)^4*(1 + x)).

a(n) = (22*n^3 + 33*n^2 + 26*n + 12) / 12 for n even.

a(n) = (22*n^3 + 33*n^2 + 26*n + 3) / 12 for n odd.

(End)

Empirical: a(n) = a(n-1) +a(n-2) -a(n-5) -a(n-6) -a(n-7) +a(n-8) +a(n-9) +a(n-10) -a(n-13) -a(n-14) +a(n-15).

Empirical: G.f. -x*(15 +92*x +275*x^2 +573*x^3 +911*x^4 +1196*x^5 +1305*x^6 +1198*x^7 +913*x^8 +574*x^9 +275*x^10 +91*x^11 +13*x^12 +x^14) / ( (1+x+x^2) *(x^4+x^3+x^2+x+1) *(x^2+1) *(1+x)^2 *(x-1)^5 ). - R. J. Mathar, Dec 15 2011

Empirical: a(n) = 2*a(n-2) +2*a(n-3) -3*a(n-5) -3*a(n-6) -2*a(n-7) +a(n-8) +4*a(n-9) +4*a(n-10) +a(n-11) -2*a(n-12) -3*a(n-13) -3*a(n-14) +2*a(n-16) +2*a(n-17) -a(n-19).

Empirical: G.f. -x*(-33 -387*x -1937*x^2 -6123*x^3 -14061*x^4 -25460*x^5 -37953*x^6 -47841*x^7 -51602*x^8 -47844*x^9 -37956*x^10 -25461*x^11 -14061*x^12 -6120*x^13 -1935*x^14 -387*x^15 -35*x^16 -x^17+x^18) / ( (x^2+1) *(x^4+x^3+x^2+x+1) *(1+x+x^2)^2 *(1+x)^3 *(x-1)^6 ). - R. J. Mathar, Dec 15 2011