cp's OEIS Frontend

Empirical: a(n) = a(n-1) +a(n-2) +2*a(n-3) +a(n-4) +12*a(n-5) +3*a(n-6) -5*a(n-7) -17*a(n-8) -11*a(n-9) -42*a(n-10) -25*a(n-11) +5*a(n-12) +38*a(n-13) +36*a(n-14) +80*a(n-15) +47*a(n-16) -a(n-17) -59*a(n-18) -61*a(n-19) -101*a(n-20) -21*a(n-21) -3*a(n-22) +71*a(n-23) +70*a(n-24) +106*a(n-25) -11*a(n-26) +8*a(n-27) -46*a(n-28) -55*a(n-29) -78*a(n-30) +17*a(n-31) -6*a(n-32) +13*a(n-33) +28*a(n-34) +36*a(n-35) -5*a(n-36) +a(n-37) -2*a(n-38) -8*a(n-39) -9*a(n-40) +a(n-44) +a(n-45)

Empirical: a(n) = (9/40)*n^5 + (19/12)*n^4 + (101/24)*n^3 + (65/12)*n^2 + (107/30)*n + 1.

Conjectures from Colin Barker, Oct 30 2018: (Start)

G.f.: x*(16 + 21*x^2 - 15*x^3 + 6*x^4 - x^5) / (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) = (53/360)*n^6 + (5/4)*n^5 + (307/72)*n^4 + (91/12)*n^3 + (683/90)*n^2 + (25/6)*n + 1.

Conjectures from Colin Barker, Oct 30 2018: (Start)

G.f.: x*(26 + 36*x + 63*x^2 - 34*x^3 + 21*x^4 - 7*x^5 + x^6) / (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) = (509/5040)*n^7 + 1*n^6 + (743/180)*n^5 + (223/24)*n^4 + (8993/720)*n^3 + (245/24)*n^2 + (502/105)*n + 1.

Conjectures from Colin Barker, Oct 30 2018: (Start)

G.f.: x*(43 + 165*x + 282*x^2 - 17*x^3 + 57*x^4 - 28*x^5 + 8*x^6 - x^7) / (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)

Empirical: a(n) = (1391/20160)*n^8 + (197/252)*n^7 + (1819/480)*n^6 + (3719/360)*n^5 + (5593/320)*n^4 + (1369/72)*n^3 + (66343/5040)*n^2 + (2257/420)*n + 1.

Conjectures from Colin Barker, Oct 31 2018: (Start)

G.f.: x*(71 + 548*x + 1373*x^2 + 623*x^3 + 222*x^4 - 83*x^5 + 36*x^6 - 9*x^7 + x^8) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

(End)