A141499 a(0)=0; a(1)=1; a(n) = triangular number at index 5*2^(n-2)-1.

0, 1, 10, 45, 190, 780, 3160, 12720, 51040, 204480, 818560, 3275520, 13104640, 52423680, 209704960, 838840320, 3355402240, 13421690880, 53686927360, 214748037120, 858992803840, 3435972526080, 13743892725760, 54975576145920, 219902315069440, 879609281249280

Offset: 0

Author

Roger L. Bagula, Aug 10 2008

Keywords

• nonn
• easy

Comments

The sequence a(n)=b(n)*(b(n)-1)/2 gives an SO(2),SO(5),SO(10),SO(20), ...

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-8).

Crossrefs

Cf. A084215.

Programs

Mathematica

Clear[a] a[0] = 1; a[1] = 2; a[2] = 5; a[n_] := a[n] = a[1]*a[n - 1]; Table[a[n]*(a[n] - 1)/2, {n, 0, 20}]
Join[{0,1},LinearRecurrence[{6,-8},{10,45},30]] (* Harvey P. Dale, May 23 2013 *)

Formula

a(0)=0. a(n)=A000217(A052549(n-1)), n>0. - R. J. Mathar, Oct 29 2008

a(n)=5*2^(-5+n)*(-4+5*2^n) for n>1. a(n)=6*a(n-1)-8*a(n-2) for n>3. G.f.: x*(1+4*x-7*x^2)/((1-2*x)*(1-4*x)). [Colin Barker, Aug 16 2012]

Extensions

Edited by N. J. A. Sloane, Aug 16 2008

Corrected the definition, which was describing an auxiliary sequence. - R. J. Mathar, Oct 29 2008

More terms from Harvey P. Dale, May 23 2013