cp's OEIS Frontend

Empirical: a(n) = 11*a(n-1) -21*a(n-2) +18*a(n-3) -114*a(n-4) +183*a(n-5) -96*a(n-6) +80*a(n-7) -65*a(n-8) +16*a(n-9)

Empirical: a(n) = 16*a(n-1) -65*a(n-2) +116*a(n-3) -387*a(n-4) -316*a(n-5) +5502*a(n-6) -6052*a(n-7) -5304*a(n-8) +10256*a(n-9) -13182*a(n-10) +1596*a(n-11) +36430*a(n-12) -48912*a(n-13) +27205*a(n-14) -2186*a(n-15) -10400*a(n-16) +7800*a(n-17) -2128*a(n-18) +192*a(n-19)

Empirical: a(n) = 22*a(n-1) -151*a(n-2) +461*a(n-3) -797*a(n-4) -4885*a(n-5) +28261*a(n-6) +53750*a(n-7) -398208*a(n-8) +360701*a(n-9) +952132*a(n-10) -5152120*a(n-11) +7572284*a(n-12) +6140578*a(n-13) -18089482*a(n-14) -653352*a(n-15) +28175814*a(n-16) +67786763*a(n-17) -392210630*a(n-18) +717516941*a(n-19) -875602031*a(n-20) +904784133*a(n-21) -930560603*a(n-22) +1037859554*a(n-23) -1035189626*a(n-24) +1256680629*a(n-25) -1842818297*a(n-26) +2256596552*a(n-27) -2217424297*a(n-28) +1613743557*a(n-29) -832569368*a(n-30) +412448612*a(n-31) -308789168*a(n-32) +241553248*a(n-33) -122269952*a(n-34) +31245376*a(n-35) -2822400*a(n-36)

Empirical: a(n) = 29*a(n-1) -296*a(n-2) +1435*a(n-3) -3427*a(n-4) -7828*a(n-5) +49592*a(n-6) +352558*a(n-7) -636195*a(n-8) -10876335*a(n-9) +33814287*a(n-10) +11969416*a(n-11) -303909144*a(n-12) +441678604*a(n-13) +3422280936*a(n-14) -8859148026*a(n-15) +852850231*a(n-16) -40652559025*a(n-17) +224135872305*a(n-18) -288423328788*a(n-19) -387179703160*a(n-20) +1064968890514*a(n-21) +233134451136*a(n-22) -1109142831534*a(n-23) +8548651106250*a(n-24) -48852225377678*a(n-25) +122390385655489*a(n-26) -195703619047481*a(n-27) +392869508379804*a(n-28) -1151435265560089*a(n-29) +2171538014535193*a(n-30) -2300815249155302*a(n-31) +1897414184113747*a(n-32) -1653214464072941*a(n-33) -137348547691080*a(n-34) +9036579264546509*a(n-35) -25618517273435769*a(n-36) +39827335881630628*a(n-37) -72361643136916710*a(n-38) +153209010276945668*a(n-39) -202596443036523874*a(n-40) +120138000799594382*a(n-41) +3287904513855923*a(n-42) -79300534420052725*a(n-43) +265881642838692769*a(n-44) -575489964002754564*a(n-45) +652989472152746893*a(n-46) -369186741991254341*a(n-47) -11325499984554073*a(n-48) +358162777599477400*a(n-49) -655515344162720269*a(n-50) +756584002882183489*a(n-51) -633515360531580266*a(n-52) +387864257955999943*a(n-53) +2512474825339141*a(n-54) -446721853742066924*a(n-55) +629695429101778274*a(n-56) -471305399541927500*a(n-57) +240594715609426998*a(n-58) -155135547438406450*a(n-59) +164328285437212760*a(n-60) -133901062998735172*a(n-61) +59901911520102136*a(n-62) -6917958139189656*a(n-63) -14599393419547920*a(n-64) +23267385598748520*a(n-65) -22070070657235008*a(n-66) +12659868667050624*a(n-67) -4121488825869312*a(n-68) +681725317178880*a(n-69) -43934723481600*a(n-70)

Empirical: a(n) = (23/360)*n^6 + (31/120)*n^5 + (17/9)*n^4 + (23/24)*n^3 + (917/360)*n^2 + (77/60)*n + 1.

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

G.f.: x*(8 + 8*x + 36*x^2 - 30*x^3 + 27*x^4 - 4*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) = (1/112)*n^8 + (79/1260)*n^7 + (121/120)*n^6 + (71/36)*n^5 + (475/48)*n^4 - (1757/180)*n^3 + (8893/840)*n^2 - (569/84)*n + 9.

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

G.f.: x*(16 + 112*x + 304*x^2 - 594*x^3 + 775*x^4 - 442*x^5 + 216*x^6 - 36*x^7 + 9*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)

Empirical: a(n) = (359/453600)*n^10 + (251/30240)*n^9 + (14533/60480)*n^8 + (583/630)*n^7 + (62303/5400)*n^6 - (4999/1440)*n^5 + (14868751/181440)*n^4 - (1038043/3780)*n^3 + (3156491/8400)*n^2 - (91003/210)*n + 362 for n>2

Empirical: a(n) = (271/5443200)*n^12 + (2327/3326400)*n^11 + (44081/1360800)*n^10 + (67031/362880)*n^9 + (1007557/226800)*n^8 + (1582/675)*n^7 + (211210703/1360800)*n^6 - (60265871/120960)*n^5 + (11265884461/5443200)*n^4 - (118533836/14175)*n^3 + (2826245099/151200)*n^2 - (113088191/3960)*n + 23503 for n>3

Empirical: a(n) = (503/209563200)*n^14 + (6527/155675520)*n^13 + (68839/23950080)*n^12 + (1220297/59875200)*n^11 + (1890089/2177280)*n^10 + (181499/362880)*n^9 + (1367211271/15240960)*n^8 - (1887455579/5443200)*n^7 + (43827922247/10886400)*n^6 - (12546180643/544320)*n^5 + (1259322375259/11975040)*n^4 - (234159554591/554400)*n^3 + (13743908156557/11642400)*n^2 - (52010645243/24024)*n + 1969115 for n>4