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0, 5, 13, 24, 38, 55, 75, 98, 124, 153, 185, 220, 258, 299, 343, 390, 440, 493, 549, 608, 670, 735, 803, 874, 948, 1025, 1105, 1188, 1274, 1363, 1455, 1550, 1648, 1749, 1853, 1960, 2070, 2183, 2299, 2418, 2540, 2665, 2793, 2924
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| This sequence is mentioned in the Guo-Niu Han's paper, chapter 6: Dictionary of the standard puzzle sequences, p. 19 (see link). - Omar E. Pol, Oct 28 2011
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LINKS
| Guo-Niu Han, Enumeration of Standard Puzzles
Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| G.f.: x*(5-2*x)/(1-x)^3. - Bruno Berselli, Feb 11 2011
a(n)=(3*n^2 + 7*n)/2.
a(n)=a(n-1)+3*n+2 (with a(0)=0) [From Vincenzo Librandi, Nov 24 2010]
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MATHEMATICA
| s=-1; lst={}; Do[s+=n+n+n-1; If[s>=0, AppendTo[lst, s]], {n, 0, 6!, 1}]; lst [Vladimir Orlovsky, Nov 04 2008]
Table[Sum[i + n - 3, {i, 4, n}], {n, 3, 50}] [Zerinvary Lajos, Jul 11 2009]
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CROSSREFS
| Cf. A000326, A005449, A045943, A115067, A140091, A059845, A140672, A140673, A140674, A140675.
The generalized pentagonal numbers b*n+3*n*(n-1)/2, for b = 1 through 12, form sequences A000326, A005449, A045943, A115067, A140090, A140091, A059845, A140672, A140673, A140674, A140675, A151542.
Cf. numbers of the form n*(d*n+10-d)/2: A008587, A056000, A028347, A014106, A028895, A045944, A186029, A007742, A022267, A033429, A022268, A049452, A186030, A135703, A152734, A139273.
Sequence in context: A075829 A119248 A114998 * A121511 A156679 A190618
Adjacent sequences: A140087 A140088 A140089 * A140091 A140092 A140093
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KEYWORD
| easy,nonn
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AUTHOR
| Omar E. Pol (info(AT)polprimos.com), May 22 2008
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