A132758 a(n) = n*(n + 31)/2.

0, 16, 33, 51, 70, 90, 111, 133, 156, 180, 205, 231, 258, 286, 315, 345, 376, 408, 441, 475, 510, 546, 583, 621, 660, 700, 741, 783, 826, 870, 915, 961, 1008, 1056, 1105, 1155, 1206, 1258, 1311, 1365, 1420, 1476, 1533, 1591, 1650

Offset

0,2

Links

Table of n, a(n) for n=0..44.

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

Formula

a(n) = n*(n+31)/2.

If we define f(n,i,r) = Sum_{k=0..n-i} binomial(n,k) * Stirling1(n-k,i) * Product_{j=0..k-1} (-r-j), then a(n) = -f(n,n-1,16) for n>=1. - Milan Janjic, Dec 20 2008

a(n) = n + a(n-1) + 15 for n>0, a(0)=0. - Vincenzo Librandi, Aug 03 2010

a(0)=0, a(1)=16, a(2)=33; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Jun 21 2012

a(n) = 16*n - floor(n/2) + floor(n^2/2). - Wesley Ivan Hurt, Jun 15 2013

From Amiram Eldar, Jan 11 2021: (Start)

Sum_{n>=1} 1/a(n) = 2*A001008(31)/(31*A002805(31)) = 290774257297357/1119127534925400.

Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/31 - 7313175618421/159875362132200. (End)

Mathematica

Table[(n(n+31))/2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 16, 33}, 50] (* Harvey P. Dale, Jun 21 2012 *)

Prog

(PARI) a(n)=n*(n+31)/2 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A000217, A001008, A002805, A056126.

Sequence in context: A041502 A041500 A361692 * A195146 A365802 A198275

Adjacent sequences: A132755 A132756 A132757 * A132759 A132760 A132761

Keyword

nonn,easy

Author

Omar E. Pol, Aug 28 2007

Status

approved