A051940 Truncated triangular numbers: n*(n+1)/2 - 3*t*(t+1)/2 with t=4.

6, 15, 25, 36, 48, 61, 75, 90, 106, 123, 141, 160, 180, 201, 223, 246, 270, 295, 321, 348, 376, 405, 435, 466, 498, 531, 565, 600, 636, 673, 711, 750, 790, 831, 873, 916, 960, 1005, 1051, 1098, 1146, 1195, 1245, 1296, 1348, 1401, 1455, 1510, 1566, 1623

Offset

8,1

Comments

Equals binomial transform of [6, 9, 1, 0, 0, 0, ...]. - Gary W. Adamson, Aug 25 2009

Links

Table of n, a(n) for n=8..57.

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

Formula

a(n) = A000217(n)-30, n>7.

a(n) = n + a(n-1) with n>8, a(8)=6. - Vincenzo Librandi, Aug 06 2010

G.f.: x^8*(6-3*x-2*x^2)/(1-x)^3. - Colin Barker, Mar 19 2012

Mathematica

Table[n*(n + 1)/2 - 30, {n, 8, 70}] (* Stefan Steinerberger, Mar 31 2006 *)
Select[Accumulate[Range[60]]-30, #>0&]  (* Harvey P. Dale, Apr 13 2011 *)

Prog

(PARI) a(n)=n*(n+1)/2-30 \\ Charles R Greathouse IV, Nov 10 2015

Crossrefs

Sequence in context: A394986 A064565 A190515 * A020207 A222170 A151762

Adjacent sequences: A051937 A051938 A051939 * A051941 A051942 A051943

Keyword

nonn,easy,nice

Author

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

Status

approved