cp's OEIS Frontend

Empirical: a(n) = 2*a(n-1) +6*a(n-2) -14*a(n-3) -14*a(n-4) +42*a(n-5) +14*a(n-6) -70*a(n-7) +70*a(n-9) -14*a(n-10) -42*a(n-11) +14*a(n-12) +14*a(n-13) -6*a(n-14) -2*a(n-15) +a(n-16)

Empirical for n mod 2 = 0: a(n) = (1/4096)*n^8 + (1/128)*n^7 + (55/512)*n^6 + (53/64)*n^5 + (1001/256)*n^4 + (185/16)*n^3 + (167/8)*n^2 + 21*n + 9

Empirical for n mod 2 = 1: a(n) = (1/4096)*n^8 + (1/128)*n^7 + (111/1024)*n^6 + (109/128)*n^5 + (8483/2048)*n^4 + (1635/128)*n^3 + (24975/1024)*n^2 + (3375/128)*n + (50625/4096).

a(n+1) = A202094(n). - R. J. Mathar, Dec 04 2014

Empirical: a(n) = 2*a(n-1) +10*a(n-2) -22*a(n-3) -44*a(n-4) +110*a(n-5) +110*a(n-6) -330*a(n-7) -165*a(n-8) +660*a(n-9) +132*a(n-10) -924*a(n-11) +924*a(n-13) -132*a(n-14) -660*a(n-15) +165*a(n-16) +330*a(n-17) -110*a(n-18) -110*a(n-19) +44*a(n-20) +22*a(n-21) -10*a(n-22) -2*a(n-23) +a(n-24)

Empirical for n mod 2 = 0: a(n) = (1/5308416)*n^12 + (5/442368)*n^11 + (407/1327104)*n^10 + (275/55296)*n^9 + (5933/110592)*n^8 + (415/1024)*n^7 + (182201/82944)*n^6 + (3715/432)*n^5 + (62483/2592)*n^4 + (2545/54)*n^3 + (731/12)*n^2 + (140/3)*n + 16

Empirical for n mod 2 = 1: a(n) = (1/5308416)*n^12 + (5/442368)*n^11 + (817/2654208)*n^10 + (2225/442368)*n^9 + (97157/1769472)*n^8 + (3455/8192)*n^7 + (3101111/1327104)*n^6 + (2080805/221184)*n^5 + (144963631/5308416)*n^4 + (24654385/442368)*n^3 + (7461475/98304)*n^2 + (3044125/49152)*n + (1500625/65536).

a(n+1) = A202096(n). - R. J. Mathar, Dec 02 2014

a(n+1) = A202092(n). - R. J. Mathar, Dec 04 2014

Empirical: a(n) = 2*a(n-1) + 4*a(n-2) - 10*a(n-3) - 5*a(n-4) + 20*a(n-5) - 20*a(n-7) + 5*a(n-8) + 10*a(n-9) - 4*a(n-10) - 2*a(n-11) + a(n-12).

Empirical for n mod 2 = 0: a(n) = (1/256)*n^6 + (11/128)*n^5 + (49/64)*n^4 + (113/32)*n^3 + (71/8)*n^2 + (23/2)*n + 6.

Empirical for n mod 2 = 1: a(n) = (1/256)*n^6 + (11/128)*n^5 + (199/256)*n^4 + (237/64)*n^3 + (2511/256)*n^2 + (1755/128)*n + (2025/256).

a(n+1)=A202093(n). - R. J. Mathar, Dec 04 2014

Empirical g.f.: x*(36 + 36*x - 36*x^2 + 124*x^4 - 20*x^5 - 115*x^6 + 40*x^7 + 56*x^8 - 26*x^9 - 11*x^10 + 6*x^11) / ((1 - x)^7*(1 + x)^5). - Colin Barker, Nov 14 2018

Empirical: a(n) = 2*a(n-1) +8*a(n-2) -18*a(n-3) -27*a(n-4) +72*a(n-5) +48*a(n-6) -168*a(n-7) -42*a(n-8) +252*a(n-9) -252*a(n-11) +42*a(n-12) +168*a(n-13) -48*a(n-14) -72*a(n-15) +27*a(n-16) +18*a(n-17) -8*a(n-18) -2*a(n-19) +a(n-20)

Empirical for n mod 2 = 0: a(n) = (1/147456)*n^10 + (23/73728)*n^9 + (13/2048)*n^8 + (77/1024)*n^7 + (1763/3072)*n^6 + (4525/1536)*n^5 + (5927/576)*n^4 + (3473/144)*n^3 + (145/4)*n^2 + (63/2)*n + 12

Empirical for n mod 2 = 1: a(n) = (1/147456)*n^10 + (23/73728)*n^9 + (941/147456)*n^8 + (1409/18432)*n^7 + (43777/73728)*n^6 + (115189/36864)*n^5 + (831857/73728)*n^4 + (169595/6144)*n^3 + (717525/16384)*n^2 + (333375/8192)*n + (275625/16384).

a(n+1)=A202095(n). - R. J. Mathar, Dec 04 2014

Empirical: a(n) = 2*a(n-1) +12*a(n-2) -26*a(n-3) -65*a(n-4) +156*a(n-5) +208*a(n-6) -572*a(n-7) -429*a(n-8) +1430*a(n-9) +572*a(n-10) -2574*a(n-11) -429*a(n-12) +3432*a(n-13) -3432*a(n-15) +429*a(n-16) +2574*a(n-17) -572*a(n-18) -1430*a(n-19) +429*a(n-20) +572*a(n-21) -208*a(n-22) -156*a(n-23) +65*a(n-24) +26*a(n-25) -12*a(n-26) -2*a(n-27) +a(n-28)

Empirical for n mod 2 = 0: a(n) = (1/339738624)*n^14 + (13/56623104)*n^13 + (697/84934656)*n^12 + (2521/14155776)*n^11 + (55639/21233664)*n^10 + (97807/3538944)*n^9 + (1143251/5308416)*n^8 + (1113683/884736)*n^7 + (1838411/331776)*n^6 + (505009/27648)*n^5 + (919427/20736)*n^4 + (265331/3456)*n^3 + (4297/48)*n^2 + (377/6)*n + 20

Empirical for n mod 2 = 1: a(n) = (1/339738624)*n^14 + (13/56623104)*n^13 + (2795/339738624)*n^12 + (5081/28311552)*n^11 + (301475/113246208)*n^10 + (178667/6291456)*n^9 + (76312715/339738624)*n^8 + (18940223/14155776)*n^7 + (2048631355/339738624)*n^6 + (1158380483/56623104)*n^5 + (647048923/12582912)*n^4 + (292086865/3145728)*n^3 + (477479275/4194304)*n^2 + (177888375/2097152)*n + (121550625/4194304).

a(n+1) = A202097(n). - R. J. Mathar, Dec 02 2014

Empirical: a(n) = 2*a(n-1) +14*a(n-2) -30*a(n-3) -90*a(n-4) +210*a(n-5) +350*a(n-6) -910*a(n-7) -910*a(n-8) +2730*a(n-9) +1638*a(n-10) -6006*a(n-11) -2002*a(n-12) +10010*a(n-13) +1430*a(n-14) -12870*a(n-15) +12870*a(n-17) -1430*a(n-18) -10010*a(n-19) +2002*a(n-20) +6006*a(n-21) -1638*a(n-22) -2730*a(n-23) +910*a(n-24) +910*a(n-25) -350*a(n-26) -210*a(n-27) +90*a(n-28) +30*a(n-29) -14*a(n-30) -2*a(n-31) +a(n-32)

Empirical for n mod 2 = 0: a(n) = (1/21743271936)*n^16 + (1/226492416)*n^15 + (89/452984832)*n^14 + (203/37748736)*n^13 + (2549/25165824)*n^12 + (1459/1048576)*n^11 + (1224205/84934656)*n^10 + (812447/7077888)*n^9 + (20096035/28311552)*n^8 + (2015611/589824)*n^7 + (3762023/294912)*n^6 + (149513/4096)*n^5 + (26016553/331776)*n^4 + (422071/3456)*n^3 + (12469/96)*n^2 + (505/6)*n + 25

Empirical for n mod 2 = 1: a(n) = (1/21743271936)*n^16 + (1/226492416)*n^15 + (535/2717908992)*n^14 + (1225/226492416)*n^13 + (185693/1811939328)*n^12 + (35725/25165824)*n^11 + (40404433/2717908992)*n^10 + (27184205/226492416)*n^9 + (8206068803/10871635968)*n^8 + (840056675/226492416)*n^7 + (476102705/33554432)*n^6 + (1052064899/25165824)*n^5 + (6239471239/67108864)*n^4 + (1265493285/8388608)*n^3 + (5650169175/33554432)*n^2 + (968932125/8388608)*n + (9845600625/268435456).

a(n+1) = A202098(n). - R. J. Mathar, Dec 02 2014