A051941 Truncated triangular pyramid numbers: a(n) = (n-7)*(n^2 + 10*n - 108)/6, n >= 8.

6, 21, 46, 82, 130, 191, 266, 356, 462, 585, 726, 886, 1066, 1267, 1490, 1736, 2006, 2301, 2622, 2970, 3346, 3751, 4186, 4652, 5150, 5681, 6246, 6846, 7482, 8155, 8866, 9616, 10406, 11237, 12110, 13026, 13986, 14991, 16042, 17140, 18286, 19481

Offset

8,1

Links

Table of n, a(n) for n=8..49.

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

Formula

a(n) = Sum_{k=8..n} k*(k+1)/2-30.

Binomial transform of [6, 15, 10, 1, 0, 0, 0, ...]. - Gary W. Adamson, Oct 22 2007

From R. J. Mathar, May 17 2008: (Start)

O.g.f.: -x^8*(-6 + 3*x + 2*x^2)/(-1+x)^4.

a(n+1) - a(n) = A051940(n+1).

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)

Mathematica

LinearRecurrence[{4, -6, 4, -1}, {6, 21, 46, 82}, 50] (* Harvey P. Dale, Oct 20 2013 *)

Prog

(PARI) a(n)=(n-7)*(n^2+10*n-108)/6 \\ Charles R Greathouse IV, Nov 10 2015
(Magma) [(n-7)*(n^2+10*n-108)/6 : n in [8..70]]; // Wesley Ivan Hurt, Apr 20 2021

Crossrefs

Cf. A000292.

Sequence in context: A081266 A087863 A212656 * A212707 A267370 A213388

Adjacent sequences: A051938 A051939 A051940 * A051942 A051943 A051944

Keyword

easy,nice,nonn

Author

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

Status

approved