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%I #21 Apr 14 2024 00:20:17
%S 6,55,153,300,496,741,1035,1378,1770,2211,2701,3240,3828,4465,5151,
%T 5886,6670,7503,8385,9316,10296,11325,12403,13530,14706,15931,17205,
%U 18528,19900,21321,22791,24310,25878,27495,29161,30876,32640,34453
%N a(n) = 49*(n*(n+1)/2) + 6.
%C "If n is a triangular number, then so are 9n+1, 25n+3 and 49n+6. (Euler, 1775)." Burton, p. 17.
%D D. M. Burton, Elementary Number Theory, Allyn and Bacon, Inc. Boston, MA, 1976, pp. 17.
%H Harry J. Smith, <a href="/A061792/b061792.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=6, a(1)=55, a(2)=153. - _Harvey P. Dale_, Apr 11 2012
%t 49*Accumulate[Range[0,40]]+6 (* or *) LinearRecurrence[{3,-3,1},{6,55,153},40] (* _Harvey P. Dale_, Apr 11 2012 *)
%o (PARI) v=[]; for(n=0,100,v=concat(v,49*(n*(n+1)/2)+6)); v
%o (PARI) for (n=0, 1000, write("b061792.txt", n, " ", 49*n*(n + 1)/2 + 6)) \\ _Harry J. Smith_, Jul 28 2009
%Y Cf. A000217.
%K easy,nonn
%O 0,1
%A _Jason Earls_, Jun 22 2001
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