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A115067
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(3*n^2-n-2)/2.
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17
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0, 4, 11, 21, 34, 50, 69, 91, 116, 144, 175, 209, 246, 286, 329, 375, 424, 476, 531, 589, 650, 714, 781, 851, 924, 1000, 1079, 1161, 1246, 1334, 1425, 1519, 1616, 1716, 1819, 1925, 2034, 2146, 2261, 2379, 2500, 2624, 2751, 2881, 3014, 3150, 3289, 3431, 3576
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Alfred Hoehn, Illustration of initial terms of A000326, A005449, A045943, A115067 [temporary remark: the case n=4 appears to be incorrect in the illustration]
Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| a(n) = (3*n+2)*(n-1)/2.
a(n+1) = n*(3*n + 5)/2. - Omar E. Pol, May 21 2008
a(n) = 3*n+a(n-1)-2 (with a(1)=0). - Vincenzo Librandi, Nov 13 2010
a(n) = A095794(-n). - Bruno Berselli, Sep 02 2011
G.f.: x^2*(4-x) / (1-x)^3 . - R. J. Mathar, Sep 02 2011
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MATHEMATICA
| lst={}; Do[AppendTo[lst, (3*n^2-n-2)/2], {n, 5!}]; lst ...and/or... s=-1; lst={}; Do[s+=n+1; AppendTo[lst, s], {n, 0, 6!, 3}]; lst [Vladimir Orlovsky, Oct 25 2008]
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PROG
| (PARI) a(n)=n*(3*n-1)/2-1 \\ Charles R Greathouse IV, Jan 27 2012
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CROSSREFS
| 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.
Sequence in context: A008052 A016438 A038427 * A009893 A027369 A008008
Adjacent sequences: A115064 A115065 A115066 * A115068 A115069 A115070
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KEYWORD
| nonn,easy
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Mar 01 2006
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EXTENSIONS
| Edited by N. J. A. Sloane, Mar 05 2006
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