A051943 Truncated triangular pyramid numbers: a(n) = Sum_{k=9..n} (k*(k+1)/2 - 45).

0, 10, 31, 64, 110, 170, 245, 336, 444, 570, 715, 880, 1066, 1274, 1505, 1760, 2040, 2346, 2679, 3040, 3430, 3850, 4301, 4784, 5300, 5850, 6435, 7056, 7714, 8410, 9145, 9920, 10736, 11594, 12495, 13440, 14430, 15466, 16549, 17680, 18860, 20090

Offset

9,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 9..1000

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

Formula

a(n) = (n+20)*(n-8)*(n-9)/6.

G.f.: x^10*(10-9*x)/(1-x)^4. - Colin Barker, Apr 30 2012

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jun 18 2012

Mathematica

LinearRecurrence[{4, -6, 4, -1}, {0, 10, 31, 64}, 50] (* Vincenzo Librandi, Jun 18 2012 *)

Prog

(Magma) I:=[0, 10, 31, 64]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..45]]; // Vincenzo Librandi, Jun 18 2012
(PARI) a(n)=(n+20)*(n-8)*(n-9)/6 \\ Charles R Greathouse IV, Nov 10 2015

Crossrefs

Cf. A000292.

Sequence in context: A209994 A211013 A085473 * A059306 A192023 A219693

Adjacent sequences: A051940 A051941 A051942 * A051944 A051945 A051946

Keyword

easy,nice,nonn

Author

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

Status

approved