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A093722
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Integers of the form (n^2 - 1) / 120.
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4
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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, 1394, 1463, 1477, 1548, 1606, 1680, 1695, 1771, 1833, 1912, 1928, 2009, 2075, 2159, 2176, 2262, 2332, 2421, 2439, 2530, 2604, 2698, 2717, 2813, 2891, 2990, 3010, 3111, 3193, 3297, 3318, 3424, 3510, 3619, 3641, 3752, 3842, 3956, 3979
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| This is "one-fifteenth of triangular numbers (integers only)" [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 04 2009]
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,20000
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FORMULA
| |A113430(n)| is the characteristic function of the numbers in A093722.
a(-1 - n) = a(n). a(n) = (A057538(n) * 2 - 1) / 120.
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MATHEMATICA
| lst={}; s=0; Do[s+=n/15; If[Floor[s]==s, AppendTo[lst, s]], {n, 0, 7!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 04 2009]
Alternate: Select[Table[(n^2-1)/120, {n, 0, 700}], IntegerQ]
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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, 20000, a=(((n\4*3 + n%4)*10 + (-1)^(n\2))^2 - 1)/120; write("b093722.txt", n, " ", a); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 18 2009]
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CROSSREFS
| Cf. A002381, A057538, A113430.
Sequence in context: A106474 A127441 A067064 * A002381 A131559 A051211
Adjacent sequences: A093719 A093720 A093721 * A093723 A093724 A093725
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Apr 13 2004
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EXTENSIONS
| Additional terms provided and alternate Mathematica program provided by Harvey P. Dale, Nov. 26, 2010
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