cp's OEIS Frontend

Empirical: a(n) = 10*a(n-1) -24*a(n-2) -2*a(n-3) +30*a(n-4) +96*a(n-5) -150*a(n-6) -108*a(n-7) +48*a(n-8) +270*a(n-9)

Empirical: a(n) = 15*a(n-1) -69*a(n-2) +66*a(n-3) +226*a(n-4) -172*a(n-5) -1192*a(n-6) +2157*a(n-7) -1714*a(n-8) -2876*a(n-9) +4966*a(n-10) +12095*a(n-11) -17584*a(n-12) +28968*a(n-13) +156*a(n-14) -2874*a(n-15) -2964*a(n-16) +15876*a(n-17) +1008*a(n-18) for n>19

Empirical: a(n) = 21*a(n-1) -155*a(n-2) +405*a(n-3) +365*a(n-4) -2996*a(n-5) -664*a(n-6) +18276*a(n-7) -22433*a(n-8) -2304*a(n-9) -9369*a(n-10) -7644*a(n-11) +222262*a(n-12) +167540*a(n-13) -1508772*a(n-14) +2046821*a(n-15) -1097976*a(n-16) +4265706*a(n-17) -2582500*a(n-18) -941886*a(n-19) -2423080*a(n-20) +19902336*a(n-21) +2548764*a(n-22) +9439760*a(n-23) +1688032*a(n-24) +1035840*a(n-25) -957120*a(n-26) +1996416*a(n-27) -115200*a(n-28) for n>31

Empirical: a(n) = 28*a(n-1) -300*a(n-2) +1417*a(n-3) -1482*a(n-4) -11436*a(n-5) +31851*a(n-6) +52359*a(n-7) -290782*a(n-8) +153075*a(n-9) +602260*a(n-10) -176604*a(n-11) -1863678*a(n-12) +536713*a(n-13) +8514601*a(n-14) -7251292*a(n-15) -64571700*a(n-16) +163992784*a(n-17) -63488599*a(n-18) +75157211*a(n-19) -574679221*a(n-20) +1117201234*a(n-21) -1103109981*a(n-22) +247796355*a(n-23) -1415805562*a(n-24) +12828520548*a(n-25) -5049431870*a(n-26) +5717879992*a(n-27) +7921013636*a(n-28) +14497424532*a(n-29) -1161322200*a(n-30) +7782865280*a(n-31) +2703305984*a(n-32) +21857003968*a(n-33) +1446146688*a(n-34) +6372675072*a(n-35) -1634756608*a(n-36) +2474711040*a(n-37) -114278400*a(n-38) +967065600*a(n-39) for n>44

Empirical recurrence of order 54 (see link above)

Empirical: a(n) = (1/12)*n^4 + 1*n^3 + (41/12)*n^2 + (7/2)*n + 1.

Conjectures from Colin Barker, Aug 25 2018: (Start)

G.f.: x*(9 - 14*x + 11*x^2 - 5*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) = (1/144)*n^6 + (5/48)*n^5 + (163/144)*n^4 + (85/16)*n^3 + (895/36)*n^2 - (65/12)*n + 3 for n>2.

Conjectures from Colin Barker, Aug 25 2018: (Start)

G.f.: x*(27 - 32*x - 56*x^2 + 164*x^3 - 159*x^4 + 85*x^5 - 32*x^6 + 9*x^7 - x^8) / (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>9.

(End)

Empirical: a(n) = (1/2880)*n^8 + (1/180)*n^7 + (25/288)*n^6 + (169/180)*n^5 + (18649/2880)*n^4 + (4247/90)*n^3 + (2719/16)*n^2 - (6649/30)*n - 17 for n>4.

Conjectures from Colin Barker, Aug 25 2018: (Start)

G.f.: x*(81 + 64*x - 1241*x^2 + 2851*x^3 - 2540*x^4 + 248*x^5 + 1398*x^6 - 1380*x^7 + 796*x^8 - 347*x^9 + 88*x^10 - x^11 - 3*x^12) / (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>13.

(End)

Empirical: a(n) = (1/86400)*n^10 + (1/5760)*n^9 + (13/3360)*n^8 + (1079/20160)*n^7 + (19031/28800)*n^6 + (35137/5760)*n^5 + (513623/8640)*n^4 + (161053/480)*n^3 + (3838487/2800)*n^2 - (614813/210)*n - 2235 for n>6

Empirical: a(n) = (1/3628800)*n^12 + (1/302400)*n^11 + (419/3628800)*n^10 + (223/120960)*n^9 + (35411/1209600)*n^8 + (20443/50400)*n^7 + (17616857/3628800)*n^6 + (6342323/120960)*n^5 + (821276033/1814400)*n^4 + (103253527/37800)*n^3 + (186412339/16800)*n^2 - (24901729/840)*n - 64275 for n>8