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A141499
a(0)=0; a(1)=1; a(n) = triangular number at index 5*2^(n-2)-1.
0
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
0,3
COMMENTS
The sequence a(n)=b(n)*(b(n)-1)/2 gives an SO(2),SO(5),SO(10),SO(20), ...
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]
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 *)
CROSSREFS
Cf. A084215.
Sequence in context: A221532 A241432 A317020 * A264553 A278641 A219709
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Aug 10 2008
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
STATUS
approved