cp's OEIS Frontend

Empirical: a(n) = 9*a(n-1) -8*a(n-2) -63*a(n-3) +250*a(n-4) -152*a(n-5) -522*a(n-6) -2735*a(n-7) +4120*a(n-8) +9651*a(n-9) +1347*a(n-10) -13682*a(n-11) -24899*a(n-12) +6443*a(n-13) +11258*a(n-14) +8578*a(n-15) -11567*a(n-16) +8480*a(n-17) +22660*a(n-18) -17587*a(n-19) +2236*a(n-20) +4536*a(n-21) -2700*a(n-22) -864*a(n-23)

Empirical: a(n) = 14*a(n-1) -52*a(n-2) +2*a(n-3) +197*a(n-4) +854*a(n-5) -1805*a(n-6) -26237*a(n-7) +86043*a(n-8) -70614*a(n-9) +170464*a(n-10) +399202*a(n-11) -2739146*a(n-12) +4095044*a(n-13) -10039780*a(n-14) +2577182*a(n-15) +24545705*a(n-16) -54040002*a(n-17) +167369490*a(n-18) -85060776*a(n-19) -28060708*a(n-20) -389208891*a(n-21) +459909922*a(n-22) +2683456378*a(n-23) -4388644180*a(n-24) -5542051151*a(n-25) -2414407341*a(n-26) +32349457536*a(n-27) +12515704412*a(n-28) -98186425408*a(n-29) -47665614177*a(n-30) +197523619448*a(n-31) +269900883869*a(n-32) -475417489889*a(n-33) -557567876049*a(n-34) +781710113042*a(n-35) +1046331021897*a(n-36) -847156975368*a(n-37) -2150199310855*a(n-38) +1141102444689*a(n-39) +2763026992524*a(n-40) -1108892309385*a(n-41) -3095005070434*a(n-42) +372805026225*a(n-43) +3825246453473*a(n-44) -381900163490*a(n-45) -3024861283470*a(n-46) +239728926637*a(n-47) +2504270286051*a(n-48) +252573497058*a(n-49) -2433283268771*a(n-50) -401711721919*a(n-51) +374998537102*a(n-52) +1383132583853*a(n-53) -540047390184*a(n-54) +123349296118*a(n-55) +364680760759*a(n-56) -406537833072*a(n-57) +329370465626*a(n-58) -927362054456*a(n-59) +96704047076*a(n-60) -90681009763*a(n-61) +444716709062*a(n-62) +392499685319*a(n-63) -228651167608*a(n-64) -64865394701*a(n-65) -27260982030*a(n-66) -5237026151*a(n-67) +5531571132*a(n-68) -124945968364*a(n-69) +62262537257*a(n-70) +50291998098*a(n-71) -17594004031*a(n-72) -1497064747*a(n-73) -14021053454*a(n-74) +17588728808*a(n-75) -464880468*a(n-76) -4736625394*a(n-77) -1543338426*a(n-78) +962821324*a(n-79) +1113573248*a(n-80) -451839972*a(n-81) -202718964*a(n-82) +36440824*a(n-83) +88759936*a(n-84) -3568528*a(n-85) -21856096*a(n-86) -1651968*a(n-87) +2626688*a(n-88) +1258624*a(n-89) -261376*a(n-90) -184320*a(n-91) +14336*a(n-92) +8192*a(n-93)

Empirical: a(n) = (23/360)*n^6 - (3/40)*n^5 + (37/18)*n^4 + (119/24)*n^3 - (3103/360)*n^2 + (997/60)*n - 9 for n>1.

Conjectures from Colin Barker, Mar 16 2018: (Start)

G.f.: x*(8 + 8*x + 12*x^2 - 32*x^3 + 63*x^4 - 16*x^5 + 5*x^6 - 2*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) = (1/112)*n^8 - (19/210)*n^7 + (59/45)*n^6 - (61/120)*n^5 - (8789/144)*n^4 + (99083/120)*n^3 - (10598579/2520)*n^2 + (1548737/140)*n - 11539 for n>6

Empirical: a(n) = (359/453600)*n^10 - (391/18144)*n^9 + (5825/12096)*n^8 - (13241/3780)*n^7 - (41189/675)*n^6 + (10637083/4320)*n^5 - (1341019765/36288)*n^4 + (7101447161/22680)*n^3 - (37771550507/25200)*n^2 + (2233774483/630)*n - 2534086 for n>12.

Empirical: a(n) = (271/5443200)*n^12 - (5527/1995840)*n^11 + (284203/2721600)*n^10 - (97799/51840)*n^9 - (4335667/259200)*n^8 + (68712079/30240)*n^7 - (50002254419/680400)*n^6 + (495395854627/362880)*n^5 - (42767475646507/2721600)*n^4 + (1367715597167/12960)*n^3 - (3261545344751/10800)*n^2 - (3687840940699/6930)*n + 4224261488 for n>20