cp's OEIS Frontend

Empirical: a(n) = 10*a(n-1) - 37*a(n-2) + 64*a(n-3) - 52*a(n-4) + 16*a(n-5) for n>6.

Conjectures from Colin Barker, Nov 03 2018: (Start)

G.f.: x*(1 - 9*x + 29*x^2 - 43*x^3 + 31*x^4 - 11*x^5) / ((1 - x)^2*(1 - 2*x)^2*(1 - 4*x)).

a(n) = (-64 - 27*2^(2+n) + 4^n + 12*(32+3*2^n)*n) / 576 for n>1.

(End)

Empirical: a(n) = 17*a(n-1) - 118*a(n-2) + 434*a(n-3) - 913*a(n-4) + 1097*a(n-5) - 696*a(n-6) + 180*a(n-7) for n>8.

Conjectures from Colin Barker, Nov 03 2018: (Start)

G.f.: x*(1 - 16*x + 103*x^2 - 346*x^3 + 656*x^4 - 710*x^5 + 425*x^6 - 124*x^7) / ((1 - x)^2*(1 - 2*x)^2*(1 - 3*x)^2*(1 - 5*x)).

a(n) = (-3375 - 525*2^(4+n) - 1300*3^n + 3*5^n + 100*(297+9*2^(2+n) + 2*3^n)*n) / 43200.

(End)

Empirical: a(n) = 26*a(n-1) - 290*a(n-2) + 1820*a(n-3) - 7073*a(n-4) + 17618*a(n-5) - 28060*a(n-6) + 27480*a(n-7) - 14976*a(n-8) + 3456*a(n-9) for n>10.

Empirical g.f.: x*(1 - 25*x + 266*x^2 - 1578*x^3 + 5738*x^4 - 13236*x^5 + 19385*x^6 - 17565*x^7 + 9271*x^8 - 2381*x^9) / ((1 - x)^2*(1 - 2*x)^2*(1 - 3*x)^2*(1 - 4*x)^2*(1 - 6*x)). - Colin Barker, Nov 03 2018

Empirical: a(n) = 37*a(n-1) - 605*a(n-2) + 5765*a(n-3) - 35523*a(n-4) + 148371*a(n-5) - 427775*a(n-6) + 849335*a(n-7) - 1134976*a(n-8) + 969292*a(n-9) - 474720*a(n-10) + 100800*a(n-11) for n>12.

Empirical g.f.: x*(1 - 36*x + 570*x^2 - 5230*x^3 + 30829*x^4 - 122268*x^5 + 332049*x^6 - 616386*x^7 + 767435*x^8 - 616428*x^9 + 296529*x^10 - 69446*x^11) / ((1 - x)^2*(1 - 2*x)^2*(1 - 3*x)^2*(1 - 4*x)^2*(1 - 5*x)^2*(1 - 7*x)). - Colin Barker, Nov 03 2018

Empirical: a(n) = 50*a(n-1) -1127*a(n-2) +15148*a(n-3) -135303*a(n-4) +846930*a(n-5) -3816041*a(n-6) +12508144*a(n-7) -29761816*a(n-8) +50647520*a(n-9) -59753232*a(n-10) +46142208*a(n-11) -20839680*a(n-12) +4147200*a(n-13) for n>14