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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.
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%I #30 Jan 01 2024 11:37:52

%S 2,3,12,65,374,2175,12672,73853,430442,2508795,14622324,85225145,

%T 496728542,2895146103,16874148072,98349742325,573224305874,

%U 3340996092915,19472752251612,113495517416753,661500352248902,3855506596076655,22471539224211024

%N 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.

%H K. J. Ramsey, <a href="http://groups.yahoo.com/group/Triangular_and_Fibonacci_Numbers/message/16">Recursive Series Problem</a> [Edited by Kenneth J. Ramsey, May 14 2011]

%H Kenneth J. Ramsey, <a href="/A108261/a108261.txt">Recursive Series Problem</a>, digest of 4 messages in Triangular_and_Fibonacci_Numbers Yahoo group, May 28, 2005 - Mar 9, 2006. [Cached copy]

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-7,1).

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

%t 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 *)

%Y Cf. A108262.

%K nonn

%O 0,1

%A _Kenneth J Ramsey_, May 29 2005

%E More terms from _Harvey P. Dale_, Mar 19 2019