cp's OEIS Frontend

Empirical: a(n) = 10*a(n-1) - 16*a(n-2) + 30*a(n-3) - 14*a(n-4) + 12*a(n-5).

Empirical g.f.: 2*x*(5 + 14*x^2 - x^3 + 6*x^4) / (1 - 10*x + 16*x^2 - 30*x^3 + 14*x^4 - 12*x^5). - Colin Barker, Aug 26 2018

Empirical: a(n) = 15*a(n-1) - 58*a(n-2) + 105*a(n-3) + 20*a(n-4) - 183*a(n-5) + 220*a(n-6) + 240*a(n-7).

Empirical g.f.: x*(15 + 156*x^2 + 101*x^3 + 157*x^4 + 460*x^5 + 240*x^6) / (1 - 15*x + 58*x^2 - 105*x^3 - 20*x^4 + 183*x^5 - 220*x^6 - 240*x^7). - Colin Barker, Aug 26 2018

Empirical: a(n) = 21*a(n-1) -141*a(n-2) +427*a(n-3) -546*a(n-4) +526*a(n-5) -2124*a(n-6) +3302*a(n-7) +2396*a(n-8) +7504*a(n-9) +580*a(n-10) +1632*a(n-11)

Empirical: a(n) = 28*a(n-1) -283*a(n-2) +1386*a(n-3) -3562*a(n-4) +4940*a(n-5) -3840*a(n-6) -14256*a(n-7) +50007*a(n-8) -26386*a(n-9) +141154*a(n-10) +250789*a(n-11) +41356*a(n-12) +274344*a(n-13) +134400*a(n-14)

Empirical: a(n) = 36*a(n-1) -505*a(n-2) +3667*a(n-3) -15271*a(n-4) +38113*a(n-5) -59621*a(n-6) +53813*a(n-7) -125335*a(n-8) +657330*a(n-9) -1326014*a(n-10) +2644047*a(n-11) +3529521*a(n-12) +7803900*a(n-13) +959690*a(n-14) +28175350*a(n-15) +27269532*a(n-16) +18725976*a(n-17) +1826832*a(n-18) +1263744*a(n-19)

Empirical: a(n) = (23/360)*n^6 + (27/40)*n^5 + (271/72)*n^4 + (65/8)*n^3 + (2101/180)*n^2 + (97/10)*n - 1 for n>1.

Conjectures from Colin Barker, Aug 26 2018: (Start)

G.f.: x*(27 + 27*x - 77*x^2 + 176*x^3 - 199*x^4 + 129*x^5 - 43*x^6 + 6*x^7) / (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>8.

(End)

Empirical: a(n) = (41/4032)*n^8 + (55/336)*n^7 + (733/480)*n^6 + (1037/120)*n^5 + (4789/192)*n^4 + (2125/48)*n^3 + (216821/5040)*n^2 + (9329/210)*n + 4 for n>2.

Conjectures from Colin Barker, Aug 26 2018: (Start)

G.f.: x*(81 + 567*x - 1370*x^2 + 1991*x^3 + 132*x^4 - 4590*x^5 + 7855*x^6 - 6900*x^7 + 3514*x^8 - 990*x^9 + 120*x^10) / (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>11.

(End)

Empirical: a(n) = (1009/907200)*n^10 + (913/36288)*n^9 + (20887/60480)*n^8 + (92987/30240)*n^7 + (835267/43200)*n^6 + (125341/1728)*n^5 + (33910279/181440)*n^4 + (8169817/45360)*n^3 + (2581069/25200)*n^2 + (35674/63)*n + 336 for n>3.

Empirical: a(n) = (761/8553600)*n^12 + (811/302400)*n^11 + (4879/97200)*n^10 + (230029/362880)*n^9 + (10666727/1814400)*n^8 + (6162019/151200)*n^7 + (76144063/388800)*n^6 + (1772311/2688)*n^5 + (230134279/194400)*n^4 + (14927389/453600)*n^3 - (7982908/51975)*n^2 + (2910398/315)*n + 7207 for n>4

Empirical: a(n) = (118519/21794572800)*n^14 + (93527/444787200)*n^13 + (611041/119750400)*n^12 + (20516659/239500800)*n^11 + (983303/907200)*n^10 + (76863193/7257600)*n^9 + (6226908251/76204800)*n^8 + (10267137467/21772800)*n^7 + (44655148529/21772800)*n^6 + (59149317869/10886400)*n^5 + (6745497467/1108800)*n^4 - (150827667029/9979200)*n^3 - (38880748217/10090080)*n^2 + (55017835997/360360)*n + 124353 for n>5