|
%I #27 Jul 30 2019 10:58:21
%S 0,1,3,7,8,14,20,29,31,42,52,66,69,85,99,118,122,143,161,185,190,216,
%T 238,267,273,304,330,364,371,407,437,476,484,525,559,603,612,658,696,
%U 745,755,806,848,902,913,969,1015,1074,1086,1147,1197,1261,1274,1340
%N Integers of the form (n^2 - 1) / 120.
%C This is "one-fifteenth of triangular numbers (integers only)". - _Vladimir Joseph Stephan Orlovsky_, Mar 04 2009
%H Harry J. Smith, <a href="/A093722/b093722.txt">Table of n, a(n) for n = 1..20000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,2,-2,0,0,-1,1).
%F |A113430(n-1)| is the characteristic function of the numbers in A093722.
%F a(-1 - n) = a(n). a(n) = (A057538(n) * 2 - 1) / 120.
%F G.f. -x^2*(1+2*x+4*x^2+x^3+4*x^4+x^6+2*x^5) / ( (1+x)^2*(x^2+1)^2*(x-1)^3 ). - _R. J. Mathar_, Jun 09 2013
%t lst={};s=0;Do[s+=n/15;If[Floor[s]==s,AppendTo[lst,s]],{n,0,7!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Mar 04 2009 *)
%t Select[Table[(n^2-1)/120,{n,0,700}],IntegerQ] (* _Harvey P. Dale_, Nov 26 2010 *)
%o (PARI) {a(n) = (((n\4 * 3 + n%4) * 10 + (-1)^(n\2))^2 - 1) / 120 } /* _Michael Somos_, Oct 17 2006 */
%o (PARI) { for (n=0, 19999, a=(((n\4*3 + n%4)*10 + (-1)^(n\2))^2 - 1)/120; write("b093722.txt", n+1, " ", a); ) } \\ Harry J. Smith, Jun 18 2009
%Y Cf. A002381, A057538, A113430.
%K nonn,easy
%O 1,3
%A _Michael Somos_, Apr 13 2004
%E More terms from _Harvey P. Dale_, Nov 26 2010
%E Offset corrected to 1 by _Ray Chandler_, Jul 29 2019
|
