cp's OEIS Frontend

Empirical: a(n) = (1/12)*n^4 + (1/3)*n^3 - (13/12)*n^2 + (8/3)*n.

Conjectures from Colin Barker, May 22 2018: (Start)

G.f.: x*(2 - 5*x + 9*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) = (1/45)*n^6 - (1/60)*n^5 - (4/9)*n^4 + (11/4)*n^3 - (206/45)*n^2 + (64/15)*n.

Conjectures from Colin Barker, May 22 2018: (Start)

G.f.: 2*x*(1 - 4*x + 11*x^2 - 9*x^3 + 15*x^4 - 6*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) = (1/453600)*n^10 + (1/2160)*n^9 + (227/60480)*n^8 - (73/1260)*n^7 + (1319/10800)*n^6 + (757/720)*n^5 - (881131/181440)*n^4 + (2207/540)*n^3 + (396407/25200)*n^2 - (6737/210)*n + 18.

Conjectures from Colin Barker, May 22 2018: (Start)

G.f.: x*(2 - 15*x + 65*x^2 - 140*x^3 + 324*x^4 - 166*x^5 + 20*x^6 - 349*x^7 + 391*x^8 - 142*x^9 + 18*x^10) / (1 - x)^11.

a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.

(End)

Empirical: a(n) = (1/64864800)*n^14 + (1/831600)*n^13 + (1643/59875200)*n^12 - (247/1995840)*n^11 - (5611/1360800)*n^10 + (61807/1814400)*n^9 + (11951/604800)*n^8 - (31427/30240)*n^7 + (10739983/2721600)*n^6 - (9433741/1814400)*n^5 + (252826879/29937600)*n^4 - (52757143/997920)*n^3 + (1595598461/10810800)*n^2 - (462725/2772)*n + 68