A093722 Integers of the form (n^2 - 1) / 120.

0, 1, 3, 7, 8, 14, 20, 29, 31, 42, 52, 66, 69, 85, 99, 118, 122, 143, 161, 185, 190, 216, 238, 267, 273, 304, 330, 364, 371, 407, 437, 476, 484, 525, 559, 603, 612, 658, 696, 745, 755, 806, 848, 902, 913, 969, 1015, 1074, 1086, 1147, 1197, 1261, 1274, 1340

Offset

1,3

Comments

This is "one-fifteenth of triangular numbers (integers only)". - Vladimir Joseph Stephan Orlovsky, Mar 04 2009

Links

Harry J. Smith, Table of n, a(n) for n = 1..20000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,2,-2,0,0,-1,1).

Formula

|A113430(n-1)| is the characteristic function of the numbers in A093722.

a(-1 - n) = a(n). a(n) = (A057538(n) * 2 - 1) / 120.

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

Mathematica

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 *)
Select[Table[(n^2-1)/120, {n, 0, 700}], IntegerQ] (* Harvey P. Dale, Nov 26 2010 *)

Prog

(PARI) {a(n) = (((n\4 * 3 + n%4) * 10 + (-1)^(n\2))^2 - 1) / 120 } /* Michael Somos, Oct 17 2006 */
(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

Crossrefs

Cf. A002381, A057538, A113430.

Sequence in context: A106474 A127441 A067064 * A309745 A002381 A131559

Adjacent sequences: A093719 A093720 A093721 * A093723 A093724 A093725

Keyword

nonn,easy

Author

Michael Somos, Apr 13 2004

Extensions

More terms from Harvey P. Dale, Nov 26 2010

Offset corrected to 1 by Ray Chandler, Jul 29 2019

Status

approved