A051937 Truncated triangular pyramid numbers: a(n) = Sum_{k=4..n} (k*(k+1)/2 - 9).

1, 7, 19, 38, 65, 101, 147, 204, 273, 355, 451, 562, 689, 833, 995, 1176, 1377, 1599, 1843, 2110, 2401, 2717, 3059, 3428, 3825, 4251, 4707, 5194, 5713, 6265, 6851, 7472, 8129, 8823, 9555, 10326, 11137, 11989, 12883, 13820, 14801, 15827, 16899, 18018

Offset

4,2

Comments

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 4..5000

Milan Janjic, Binomial Coefficients and Enumeration of Restricted Words, Journal of Integer Sequences, 2016, Vol 19, #16.7.3.

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

Formula

a(n) = (1/6)*(n-3)*(n^2+6*n-34).

G.f.: x^4*(1+3*x-3*x^2)/(1-x)^4. - Colin Barker, Mar 19 2012

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Apr 28 2012

a(n) = A000290(n-4) + A005286(n-4). - Ivan N. Ianakiev, Dec 24 2019

Mathematica

CoefficientList[Series[(1+3*x-3*x^2)/(1-x)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Apr 28 2012 *)
LinearRecurrence[{4, -6, 4, -1}, {1, 7, 19, 38}, 50] (* Harvey P. Dale, Aug 12 2012 *)

Prog

(Magma) I:=[1, 7, 19, 38]; [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, Apr 28 2012
(PARI) a(n)=(n-3)*(n^2+6*n-34)/6 \\ Charles R Greathouse IV, Nov 10 2015

Crossrefs

Cf. A000292.

Sequence in context: A155357 A155248 A027452 * A119327 A152728 A252789

Adjacent sequences: A051934 A051935 A051936 * A051938 A051939 A051940

Keyword

easy,nice,nonn

Author

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

Status

approved