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A051942 Truncated triangular numbers: a(n) = n*(n+1)/2-3*t*(t+1)/2, t = 5. 8
0, 10, 21, 33, 46, 60, 75, 91, 108, 126, 145, 165, 186, 208, 231, 255, 280, 306, 333, 361, 390, 420, 451, 483, 516, 550, 585, 621, 658, 696, 735, 775, 816, 858, 901, 945, 990, 1036, 1083, 1131, 1180, 1230, 1281, 1333, 1386, 1440, 1495, 1551, 1608, 1666 (list; graph; refs; listen; history; text; internal format)
OFFSET

9,2

LINKS

Table of n, a(n) for n=9..58.

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

FORMULA

a(n) = (n^2+n-90)/2 = (n-9)*(n+10)/2 = n*(n+1)/2 - 45.

a(n) = +3*a(n-1) -3*a(n-2) +1*a(n-3), n>=13.

a(n) = n+a(n-1) (with a(9)=0). - Vincenzo Librandi, Aug 06 2010

G.f.: x^10*(10-9*x)/(1-x)^3.

If we define f(n,i,a) = Sum_{k=0..n-i} (binomial(n,k)*stirling1(n-k,i)*Product_{j=0..k-1} (-a-j)), then a(n+9) = -f(n,n-1,10), for n>=1. - Milan Janjic, Dec 20 2008

a(n) = 10n - floor(n/2) + floor(n^2/2). - Wesley Ivan Hurt, Jun 15 2013

EXAMPLE

a(10) = 10 + 0 = 10; a(11) = 11 + 10 = 21; a(12) = 12 + 21 = 33.

MAPLE

A051942:=n->(n^2+n-90)/2: seq(A051942(n), n=9..80); # Wesley Ivan Hurt, Jan 28 2017

MATHEMATICA

Table[n (n + 1)/2 - 45, {n, 9, 100}] (* Vladimir Joseph Stephan Orlovsky, Jun 15 2011 *)

#-45&/@Drop[Accumulate[Range[60]], 8] (* Harvey P. Dale, Jul 24 2011 *)

LinearRecurrence[{3, -3, 1}, {0, 10, 21}, 60] (* Harvey P. Dale, Mar 25 2015 *)

PROG

(PARI) a(n)=(n-9)*(n+10)/2;

CROSSREFS

a(n) = A000217(n)-45, n>8.

Cf. A000096, A056121, A079664, A001477.

Sequence in context: A184989 A072806 A189402 * A250664 A082581 A075846

Adjacent sequences:  A051939 A051940 A051941 * A051943 A051944 A051945

KEYWORD

easy,nice,nonn

AUTHOR

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

EXTENSIONS

More terms from Zerinvary Lajos, Oct 01 2006

STATUS

approved

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Last modified September 24 18:42 EDT 2017. Contains 292433 sequences.