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A051936 Truncated triangular numbers: a(n) = n*(n+1)/2 - 9. 7
1, 6, 12, 19, 27, 36, 46, 57, 69, 82, 96, 111, 127, 144, 162, 181, 201, 222, 244, 267, 291, 316, 342, 369, 397, 426, 456, 487, 519, 552, 586, 621, 657, 694, 732, 771, 811, 852, 894, 937, 981, 1026, 1072, 1119, 1167, 1216, 1266, 1317, 1369, 1422, 1476 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,2

COMMENTS

Equals binomial transform of [1, 5, 1, 0, 0, 0, ...]. - Gary W. Adamson, Apr 30 2008

Numbers m > 0 such that 8m+73 is a square. - Bruce J. Nicholson, Jul 29 2017

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 4..10000

C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube [Dead link]

C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube [Cached copy, May 15 2013]

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

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

a(n) = n + a(n-1) for n>4, a(4)=1. - Vincenzo Librandi, Aug 06 2010

a(n) = 2*A000217(n-3) - A000217(n-6), with A000217(-2)=1, A000217(-1)=0. - Bruno Berselli, Oct 13 2016

EXAMPLE

Illustration of the initial terms:

                                                          .

                              .                         .   .

      .                     .   .                     o   o   o

    .   .                 o   o   o                 o   o   o   o

  .   o   .             .   o   o   .             .   o   o   o   .

.   .   .   .         .   .   o   .   .         .   .   o   o   .   .

----------------------------------------------------------------------

      1                       6                           12

----------------------------------------------------------------------

- Bruno Berselli, Oct 13 2016

MATHEMATICA

Table[n*(n + 1)/2 - 9, {n, 4, 60}] (* Stefan Steinerberger, Mar 25 2006 *)

k = 4; NestList[(k++; # + k) &, 1, 45] (* Robert G. Wilson v, Feb 02 2011 *)

Drop[Accumulate[Range[60]]-9, 3] (* Harvey P. Dale, Jan 16 2012 *)

PROG

(Haskell)

a051936 = (subtract 9) . a000217

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

-- Reinhard Zumkeller, Oct 25 2012

(PARI) a(n)=n*(n+1)/2-9 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A000217.

Sequence in context: A187391 A081846 A078816 * A215342 A146923 A256977

Adjacent sequences:  A051933 A051934 A051935 * A051937 A051938 A051939

KEYWORD

nonn,nice,easy

AUTHOR

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

STATUS

approved

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Last modified September 18 12:00 EDT 2019. Contains 327170 sequences. (Running on oeis4.)