A051938 Truncated triangular numbers: a(n) = n*(n+1)/2 - 18.

3, 10, 18, 27, 37, 48, 60, 73, 87, 102, 118, 135, 153, 172, 192, 213, 235, 258, 282, 307, 333, 360, 388, 417, 447, 478, 510, 543, 577, 612, 648, 685, 723, 762, 802, 843, 885, 928, 972, 1017, 1063, 1110, 1158, 1207, 1257, 1308, 1360, 1413, 1467, 1522, 1578

Offset: 6

Author

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

Keywords

• easy
• nonn

Comments

If a 3-set Y and a 3-set Z, having one element in common, are subsets of an n-set X then a(n+2) is the number of 3-subsets of X intersecting both Y and Z. - Milan Janjic, Oct 03 2007

Links

• Colin Barker, Table of n, a(n) for n = 6..1000
• Milan Janjic, Two Enumerative Functions.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

a(n) = A000217(n) - 18 for n>5.

Cf. A155212. - Vincenzo Librandi, Jan 22 2009

Programs

Mathematica

Drop[Accumulate[Range[60]]-18,5] (* Harvey P. Dale, Dec 08 2017 *)

PARI

Vec(x^6*(3*x^2-x-3)/(x-1)^3 + O(x^100)) \\ Colin Barker, Mar 18 2015

Formula

a(n) = n + a(n-1) (with a(6)=3). - Vincenzo Librandi, Aug 06 2010

G.f.: x^6*(3*x^2-x-3) / (x-1)^3. - Colin Barker, Mar 18 2015

Sum_{n>=6} 1/a(n) = 4423/6120 + 2*Pi*tan(sqrt(145)*Pi/2)/sqrt(145). - Amiram Eldar, Dec 13 2022