A244373 a(n) = A242107(n+1) * A242107(n-1) * (1 + mod(n,2)).

1, 0, 1, 2, -1, 4, 3, 4, 15, -14, 65, 224, -143, 1824, 1441, 12882, 50959, -151420, 898979, 5337220, 20799, 188372002, -733599, 6648401344, 39471457217, -234341035456, 2785299158305, 24790831385826, 98497628929855, 4377139749257604, -12158771603059997

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..232

Formula

Given elliptic curve "58a1" : y^2 + x * y = x^3 - x^2 - x + 1, then the n th multiple of point [0, 1] is [a(n) / A242107(n)^2, A242107(n+2)^2 * A242107(n-4) / A242107(n)^3].

a(n) = a(-n) for all n in Z.

a(n+1) * A242107(n+4) = a(n+3) * A242107(n) for all n in Z.

0 = a(n)*a(n+7) + a(n+1)*a(n+6) - 2*a(n+2)*a(n+5) - 2*a(n+3)*a(n+4) for all n in Z.

0 = 2*a(n)*a(n+6) - a(n+1)*a(n+5) + 2*a(n+2)*a(n+4) - a(n+3)*a(n+3) for all even n in Z.

0 = a(n)*a(n+6) - 2*a(n+1)*a(n+5) + a(n+2)*a(n+4) - 2*a(n+3)*a(n+3) for all odd n in Z.

Mathematica

Join[{1, 0}, RecurrenceTable[{a[n] == (-a[n-6]*a[n-1] + 2*a[n-2]*a[n-5] + 2*a[n-3]*a[n-4])/a[n-7], a[2] == 1, a[3] == 2, a[4] == -1, a[5] == 4, a[6] == 3, a[7] == 4, a[8] == 15}, a, {n, 2, 50}]] (* G. C. Greubel, Aug 05 2018 *)

Prog

(PARI) {a(n) = if( n==0, 1, n=abs(n); numerator( ellmul( ellinit([1, -1, 0, -1, 1]), [0, 1], n)[1]))};
(Magma) I:=[1, 2, -1, 4, 3, 4, 15]; [n le 7 select I[n] else (-Self(n-6)*Self(n -1) + 2*Self(n-2)*Self(n-5) + 2*Self(n-3)*Self(n-4))/Self(n-7): n in [1..30]]; // G. C. Greubel, Aug 05 2018

Crossrefs

Cf. A242107.

Sequence in context: A324757 A144334 A141210 * A107640 A030065 A362939

Adjacent sequences: A244370 A244371 A244372 * A244374 A244375 A244376

Keyword

sign

Author

Michael Somos, Aug 22 2014

Status

approved