cp's OEIS Frontend

Empirical: a(n) = 4*a(n-1) -5*a(n-2) +5*a(n-4) -4*a(n-5) +a(n-6)

Contribution from Vaclav Kotesovec, Sep 01 2012: (Start)

Empirical: G.f.: 4*x^3*(7 + 10*x + 5*x^2)/((1-x)^5*(1+x))

Empirical: a(n) = 1/4 - 10*n/3 + 23*n^2/3 - 20*n^3/3 + 11*n^4/6 - (-1)^n/4

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Empirical: a(n) = 4*a(n-1) -4*a(n-2) -4*a(n-3) +10*a(n-4) -4*a(n-5) -4*a(n-6) +4*a(n-7) -a(n-8)

Contribution from Vaclav Kotesovec, Sep 01 2012: (Start)

Empirical: G.f.: 8*x^3*(3 + 29*x + 63*x^2 + 43*x^3 + 14*x^4)/((1-x)^6*(1+x)^2)

Empirical: a(n) = -2 + 257*n/15 - 109*n^2/3 + 106*n^3/3 - 47*n^4/3 + 38*n^5/15 + (-1)^n*(2-n)

(End)

Empirical: a(n) = 4*a(n-1) -3*a(n-2) -8*a(n-3) +14*a(n-4) -14*a(n-6) +8*a(n-7) +3*a(n-8) -4*a(n-9) +a(n-10)

Contribution from Vaclav Kotesovec, Sep 01 2012: (Start)

Empirical: G.f.: 8*x^3*(1 + 69*x + 394*x^2 + 790*x^3 + 829*x^4 + 357*x^5 + 84*x^6)/((1-x)^7*(1+x)^3)

Empirical: a(n) = 51/4 - 913*n/10 + 69203*n^2/360 - 602*n^3/3 + 1007*n^4/9 - 473*n^5/15 + 631*n^6/180 + (-1)^n*(-51/4 + 25*n/2 - 23*n^2/8)

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Empirical: a(n) = 4*a(n-1) -2*a(n-2) -12*a(n-3) +17*a(n-4) +8*a(n-5) -28*a(n-6) +8*a(n-7) +17*a(n-8) -12*a(n-9) -2*a(n-10) +4*a(n-11) -a(n-12).

From Vaclav Kotesovec, Sep 01 2012: (Start)

Empirical: G.f.: 8*x^4*(105 + 1558*x + 6383*x^2 + 13396*x^3 + 14367*x^4 + 9654*x^5 + 2937*x^6 + 528*x^7)/((1-x)^8*(1+x)^4).

Empirical: a(n) = -297/4 + 13961*n/28 - 32551*n^2/30 + 54158*n^3/45 - 4625*n^4/6 + 5189*n^5/18 - 872*n^6/15 + 1529*n^7/315 + (-1)^n*(297/4 - 439*n/4 + 99*n^2/2 - 7*n^3).

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Contribution from Vaclav Kotesovec, Sep 01 2012: (Start)

Empirical: Recurrence: a(n) = a(n-14) - 4*a(n-13) + a(n-12) + 16*a(n-11) - 19*a(n-10) - 20*a(n-9) + 45*a(n-8) - 45*a(n-6) + 20*a(n-5) + 19*a(n-4) - 16*a(n-3) - a(n-2) + 4*a(n-1).

Empirical: G.f.: 16*x^4*(49 + 2335*x + 18119*x^2 + 65761*x^3 + 125593*x^4 + 154411*x^5 + 109333*x^6 + 52763*x^7 + 12090*x^8 + 1722*x^9)/((1-x)^9*(1+x)^5).

Empirical: a(n) = 6421/16 - 581677*n/210 + 2022619*n^2/315 - 340262*n^3/45 + 1915471*n^4/360 - 106466*n^5/45 + 29363*n^6/45 - 31916*n^7/315 + 16943*n^8/2520 + (-1)^n*(-6421/16 + 1645*n/2 - 557*n^2 + 155*n^3 - 123*n^4/8).

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From Vaclav Kotesovec, Sep 01 2012: (Start)

Empirical: Recurrence: a(n) = a(n-17) - 5*a(n-16) + 4*a(n-15) + 20*a(n-14) - 40*a(n-13) - 16*a(n-12) + 100*a(n-11) - 44*a(n-10) - 110*a(n-9) + 110*a(n-8) + 44*a(n-7) - 100*a(n-6) + 16*a(n-5) + 40*a(n-4) - 20*a(n-3) - 4*a(n-2) + 5*a(n-1)

Empirical: G.f.: 8*x^4*(48 + 10841*x + 164036*x^2 + 980511*x^3 + 2981932*x^4 + 5786766*x^5 + 6924788*x^6 + 5849090*x^7 + 3007252*x^8 + 1111577*x^9 + 201048*x^10 + 23391*x^11)/((1-x)^10*(1+x)^6)

Empirical: a(n) = -31395/16 + 31519*n/2 - 50452903*n^2/1260 + 13521503*n^3/270 - 4517641*n^4/120 + 224087*n^5/12 - 93658*n^6/15 + 60857*n^7/45 - 428119*n^8/2520 + 503*n^9/54 + (-1)^n*(31395/16 - 55203*n/10 + 20473*n^2/4 - 4275*n^3/2 + 3349*n^4/8 - 629*n^5/20)

(End)