A157326 -id:A157326 - cp's OEIS frontend

A157324 a(n) = 36*n^2 + n.

37, 146, 327, 580, 905, 1302, 1771, 2312, 2925, 3610, 4367, 5196, 6097, 7070, 8115, 9232, 10421, 11682, 13015, 14420, 15897, 17446, 19067, 20760, 22525, 24362, 26271, 28252, 30305, 32430, 34627, 36896, 39237, 41650, 44135, 46692, 49321, 52022

Offset: 1

Vincenzo Librandi, Feb 27 2009

The identity (10368*n^2 + 288*n + 1)^2 - (36*n^2 + n)*(1728*n + 24)^2 = 1 can be written as A157326(n)^2 - a(n)*A157325(n)^2 = 1.

This is the case s=6 of the identity (8*n^2*s^4 + 8*n*s^2 + 1)^2 - (n^2*s^2 + n)*(8*n*s^3 + 4*s)^2 = 1. - Vincenzo Librandi, Jan 26 2012

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Vincenzo Librandi, X^2-AY^2=1
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A157325, A157326.

I:=[37, 146, 327]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jan 26 2012

LinearRecurrence[{3,-3,1},{37,146,327},50] (* Vincenzo Librandi, Jan 26 2012 *)
Table[36n^2+n,{n,50}] (* Harvey P. Dale, Mar 09 2019 *)

for(n=1, 40, print1(36*n^2 + n", ")); \\ Vincenzo Librandi, Jan 26 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 26 2012

G.f.: x*(-37 - 35*x)/(x-1)^3. - Vincenzo Librandi, Jan 26 2012

A157325 a(n) = 1728*n + 24.

Original entry on oeis.org

1752, 3480, 5208, 6936, 8664, 10392, 12120, 13848, 15576, 17304, 19032, 20760, 22488, 24216, 25944, 27672, 29400, 31128, 32856, 34584, 36312, 38040, 39768, 41496, 43224, 44952, 46680, 48408, 50136, 51864, 53592, 55320, 57048, 58776

Offset: 1

Vincenzo Librandi, Feb 27 2009

The identity (10368*n^2 + 288*n + 1)^2 - (36*n^2 + n)*(1728*n + 24)^2 = 1 can be written as A157326(n)^2 - A157324(n)*a(n)^2 = 1 (see also second part of the comment at A157324). - Vincenzo Librandi, Jan 26 2012

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Vincenzo Librandi, X^2-AY^2=1
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A157324, A157326.

I:=[1752, 3480]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]]; // Vincenzo Librandi, Jan 26 2012

LinearRecurrence[{2,-1},{1752,3480},50] (* Vincenzo Librandi, Jan 26 2012 *)
1728*Range[40]+24 (* Harvey P. Dale, Feb 28 2016 *)

for(n=1, 22, print1(1728*n + 24", ")); \\ Vincenzo Librandi, Jan 26 2012

G.f.: x*(1752 - 24*x)/(1-x)^2. - Vincenzo Librandi, Jan 26 2012

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jan 26 2012

cp's OEIS Frontend

A157324 a(n) = 36*n^2 + n.

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