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A014493
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Odd triangular numbers.
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11
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1, 3, 15, 21, 45, 55, 91, 105, 153, 171, 231, 253, 325, 351, 435, 465, 561, 595, 703, 741, 861, 903, 1035, 1081, 1225, 1275, 1431, 1485, 1653, 1711, 1891, 1953, 2145, 2211, 2415, 2485, 2701, 2775, 3003, 3081, 3321, 3403, 3655, 3741, 4005, 4095, 4371, 4465, 4753, 4851
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Odd numbers of the form n*(n+1)/2.
For n such that n(n+1)/2 is odd see A042963 (congruent to 1 or 2 mod 4).
Even central polygonal numbers minus 1. - Omar E. Pol, Aug 17 2011
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Triangular Number
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FORMULA
| a(n) = (2*n-1)*(2*n-1-(-1)^n)/2. [From Ant King, Nov 17 2010]
a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5). [From Ant King, Nov 17 2010]
G.f.:x*(-1-x^4-2*x^3-10*x^2-2*x)/((x+1)^2*(x-1)^3) [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009]
a(n) = A000217(A042963(n)). [Reinhard Zumkeller, Feb 14 2012, Oct 04 2004]
a(n) = A193868(n) - 1. - Omar E. Pol, Aug 17 2011
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MATHEMATICA
| Select[ Table[n(n + 1)/2, {n, 93}], OddQ[ # ] &] (from Robert G. Wilson v Nov 05 2004).
LinearRecurrence[{1, 2, -2, -1, 1}, {1, 3, 15, 21, 45}, 50] (* From Harvey P. Dale, June 19 2011 *)
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PROG
| (MAGMA) [(2*n-1)*(2*n-1-(-1)^n)/2: n in [1..50]]; // Vincenzo Librandi, Aug 18 2011
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CROSSREFS
| Cf. A000217, A014494, A042963.
Sequence in context: A036897 A129966 A110172 * A147025 A147017 A171570
Adjacent sequences: A014490 A014491 A014492 * A014494 A014495 A014496
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Mohammad K. Azarian (ma3(AT)evansville.edu)
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EXTENSIONS
| More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
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