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A051936 Truncated triangular numbers: a(n) = n*(n+1)/2 - 9. 7

%I

%S 1,6,12,19,27,36,46,57,69,82,96,111,127,144,162,181,201,222,244,267,

%T 291,316,342,369,397,426,456,487,519,552,586,621,657,694,732,771,811,

%U 852,894,937,981,1026,1072,1119,1167,1216,1266,1317,1369,1422,1476

%N Truncated triangular numbers: a(n) = n*(n+1)/2 - 9.

%C Equals binomial transform of [1, 5, 1, 0, 0, 0, ...]. - _Gary W. Adamson_, Apr 30 2008

%C Numbers m > 0 such that 8m+73 is a square. - _Bruce J. Nicholson_, Jul 29 2017

%H Reinhard Zumkeller, <a href="/A051936/b051936.txt">Table of n, a(n) for n = 4..10000</a>

%H C. Rossiter, <a href="http://noticingnumbers.net/300SeriesCube.htm">Depictions, Explorations and Formulas of the Euler/Pascal Cube</a> [Dead link]

%H C. Rossiter, <a href="/A005581/a005581.pdf">Depictions, Explorations and Formulas of the Euler/Pascal Cube</a> [Cached copy, May 15 2013]

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F G.f.: x^4*(-1-3*x+3*x^2) / (x-1)^3.

%F a(n) = n + a(n-1) for n>4, a(4)=1. - _Vincenzo Librandi_, Aug 06 2010

%F a(n) = 2*A000217(n-3) - A000217(n-6), with A000217(-2)=1, A000217(-1)=0. - _Bruno Berselli_, Oct 13 2016

%e Illustration of the initial terms:

%e .

%e . . .

%e . . . o o o

%e . . o o o o o o o

%e . o . . o o . . o o o .

%e . . . . . . o . . . . o o . .

%e ----------------------------------------------------------------------

%e 1 6 12

%e ----------------------------------------------------------------------

%e - _Bruno Berselli_, Oct 13 2016

%t Table[n*(n + 1)/2 - 9, {n, 4, 60}] (* _Stefan Steinerberger_, Mar 25 2006 *)

%t k = 4; NestList[(k++; # + k) &, 1, 45] (* _Robert G. Wilson v_, Feb 02 2011 *)

%t Drop[Accumulate[Range[60]]-9,3] (* _Harvey P. Dale_, Jan 16 2012 *)

%o (Haskell)

%o a051936 = (subtract 9) . a000217

%o a051936_list = scanl (+) 1 [5..]

%o -- _Reinhard Zumkeller_, Oct 25 2012

%o (PARI) a(n)=n*(n+1)/2-9 \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A000217.

%K nonn,nice,easy

%O 4,2

%A Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 21 1999

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Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)