A108261 2nd order recursive series having the property that the product of any two adjacent terms is a triangular number, T(b) = b(b+1)/2 where b equals term a(n) of related series A108262.

2, 3, 12, 65, 374, 2175, 12672, 73853, 430442, 2508795, 14622324, 85225145, 496728542, 2895146103, 16874148072, 98349742325, 573224305874, 3340996092915, 19472752251612, 113495517416753, 661500352248902, 3855506596076655, 22471539224211024

Offset

0,1

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

K. J. Ramsey, Recursive Series Problem [Edited by Kenneth J. Ramsey, May 14 2011]

Kenneth J. Ramsey, Recursive Series Problem, digest of 4 messages in Triangular_and_Fibonacci_Numbers Yahoo group, May 28, 2005 - Mar 9, 2006. [Cached copy]

Index entries for linear recurrences with constant coefficients, signature (7,-7,1).

Formula

a(n) = 6*a(n-1) - a(n-2) - 4.

Mathematica

RecurrenceTable[{a[0]==2, a[1]==3, a[n]==6a[n-1]-a[n-2]-4}, a, {n, 20}] (* Harvey P. Dale, Mar 19 2019 *)
LinearRecurrence[{7, -7, 1}, {2, 3, 12}, 30] (* Harvey P. Dale, Mar 05 2025 *)

Crossrefs

Cf. A108262.

Sequence in context: A032133 A155579 A353163 * A013152 A012911 A264726

Adjacent sequences: A108258 A108259 A108260 * A108262 A108263 A108264

Keyword

nonn,changed

Author

Kenneth J Ramsey, May 29 2005

Extensions

More terms from Harvey P. Dale, Mar 19 2019

Status

approved