A350980 -id:A350980 - cp's OEIS frontend

A350981 Union of A350979 and A350980.

1, 17, 652, 4700, 165985, 1194161, 42159916, 303312572, 10708453057, 77040199505, 2719904916940, 19567907362076, 690845140450081, 4970171429768177, 175471945769404012, 1262403975253755260, 44569183380288169345, 320645639543024068241, 11320397106647425609996, 81442730039952859578332

Offset: 1

N. J. A. Sloane, Mar 06 2022

Arises in studying the equation x^3 - 7*y^2 = 1.

P.-F. Teilhet, Query 2228, L'Intermédiaire des Mathématiciens, 11 (1904), 44-45.

Index entries for linear recurrences with constant coefficients, signature (1,254,-254,-1,1).

Cf. A350979, A350980.

From Chai Wah Wu, Mar 06 2022: (Start)
a(n) = a(n-1) + 254*a(n-2) - 254*a(n-3) - a(n-4) + a(n-5) for n > 5.
G.f.: x*(4*x^4 + 16*x^3 - 381*x^2 - 16*x - 1)/((x - 1)*(x^2 - 16*x + 1)*(x^2 + 16*x + 1)). (End)
4*a(n) = 7*( -A077412(n)+17*A077412(n-1)) -3*( (-1)^n*A077412(n)+15*(-1)^(n-1)*A077412(n-1)) -6 . - R. J. Mathar, Mar 09 2022

A350979 a(0)=1, a(1)=652, thereafter a(n) = 254*a(n-1)-a(n-2)+378.

Original entry on oeis.org

1, 652, 165985, 42159916, 10708453057, 2719904916940, 690845140450081, 175471945769404012, 44569183380288169345, 11320397106647425609996, 2875336295905065816770017, 730324098762780070033974700, 185499445749450232722812804161, 47116128896261596331524418282572, 11967311240204696017974479430969505

Offset: 0

N. J. A. Sloane, Mar 06 2022

nonn

Arises in studying the equation x^3 - 7*y^2 = 1.

P.-F. Teilhet, Query 2228, L'Intermédiaire des Mathématiciens, 11 (1904), 44-45.

Index entries for linear recurrences with constant coefficients, signature (255,-255,1).

Cf. A144929, A350980, A350981, A350982.

From Chai Wah Wu, Mar 07 2022: (Start)
a(n) = 255*a(n-1) - 255*a(n-2) + a(n-3) for n > 3.
G.f.: x*(20*x^2 - 397*x - 1)/((x - 1)*(x^2 - 254*x + 1)). (End)

A350982 a(0)=0, a(1)=49, thereafter a(n) = 14*a(n-1)-a(n-2)+42.

Original entry on oeis.org

0, 49, 728, 10185, 141904, 1976513, 27529320, 383434009, 5340546848, 74384221905, 1036038559864, 14430155616233, 200986140067440, 2799375805327969, 38990275134524168, 543064476078010425, 7563912389957621824, 105351708983328695153, 1467360013376644110360, 20437688478289688849929

Offset: 0

N. J. A. Sloane, Mar 08 2022

nonn

Arises in studying the equation x^3 - 7*y^2 = 1.

P.-F. Teilhet, Query 2228, L'Intermédiaire des Mathématiciens, 11 (1904), 44-45.

Cf. A144929, A350979, A350980, A350981.

cp's OEIS Frontend

A350981 Union of A350979 and A350980.

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A350979 a(0)=1, a(1)=652, thereafter a(n) = 254*a(n-1)-a(n-2)+378.

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Formula

A350982 a(0)=0, a(1)=49, thereafter a(n) = 14*a(n-1)-a(n-2)+42.

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