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A051939 Truncated triangular pyramid numbers: a(n) = Sum_{k=6..n}(k*(k+1)/2 - 18). 1
3, 13, 31, 58, 95, 143, 203, 276, 363, 465, 583, 718, 871, 1043, 1235, 1448, 1683, 1941, 2223, 2530, 2863, 3223, 3611, 4028, 4475, 4953, 5463, 6006, 6583, 7195, 7843, 8528, 9251, 10013, 10815, 11658, 12543, 13471, 14443, 15460, 16523, 17633, 18791 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,1

LINKS

Table of n, a(n) for n=6..48.

Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).

FORMULA

a(n) = (1/6)*(n-5)*(n^2+8*n-66).

Equals binomial transform of (3, 10, 8, 1, 0, 0, 0,...). - Gary W. Adamson, Jul 03 2008

a(6)=3, a(7)=13, a(8)=31, a(9)=58, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)- a(n-4). - Harvey P. Dale, Oct 22 2011

G.f.: (-3*x^2+x+3)/(x-1)^4. - Harvey P. Dale, Oct 22 2011

MAPLE

A051939:=n->(n-5)*(n^2+8*n-66)/6; seq(A051939(k), k=6..100); # Wesley Ivan Hurt, Nov 04 2013

MATHEMATICA

Table[(1/6)*(n - 5)*(n^2 + 8*n - 66), {n, 6, 60}] (* Stefan Steinerberger, Mar 31 2006 *)

LinearRecurrence[{4, -6, 4, -1}, {3, 13, 31, 58}, 60] (* Harvey P. Dale, Oct 22 2011 *)

PROG

(PARI) a(n)=(n-5)*(n^2+8*n-66)/6 \\ Charles R Greathouse IV, Nov 10 2015

CROSSREFS

Cf. A000292.

Sequence in context: A179027 A145907 A054554 * A257764 A146728 A082709

Adjacent sequences:  A051936 A051937 A051938 * A051940 A051941 A051942

KEYWORD

easy,nice,nonn

AUTHOR

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

STATUS

approved

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Last modified October 22 07:29 EDT 2019. Contains 328315 sequences. (Running on oeis4.)