A100175 Structured triakis tetrahedral numbers (vertex structure 4).

1, 8, 30, 76, 155, 276, 448, 680, 981, 1360, 1826, 2388, 3055, 3836, 4740, 5776, 6953, 8280, 9766, 11420, 13251, 15268, 17480, 19896, 22525, 25376, 28458, 31780, 35351, 39180, 43276, 47648, 52305, 57256, 62510, 68076, 73963, 80180, 86736, 93640, 100901, 108528

Offset

1,2

Comments

Equals binomial transform of [1, 7, 15, 9, 0, 0, 0, ...] where (1, 7, 15, 9) = row 3 of triangle A038763. - Gary W. Adamson, Jul 19 2008

Equals convolution square of 1, 4, 7, 10, 13, 16, 19, ..., A016777. - Gary W. Adamson, Jul 28 2009

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

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

Formula

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

G.f.: x*(2*x+1)^2 / ( (x-1)^4 ).

Mathematica

CoefficientList[Series[x (2x+1)^2/((x-1)^4), {x, 0, 50}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 1, 8, 30}, 50] (* Harvey P. Dale, Mar 18 2023 *)

Prog

(Magma) [(3*n^3-3*n^2+2*n)/2: n in [1..50] ]; // Vincenzo Librandi, Aug 02 2011

Crossrefs

Cf. A000578 (alternate vertex), A100145 for more on structured numbers.

Cf. A038763.

Sequence in context: A131769 A055832 A195753 * A063489 A299284 A348461

Adjacent sequences: A100172 A100173 A100174 * A100176 A100177 A100178

Keyword

easy,nonn

Author

James A. Record (james.record(AT)gmail.com), Nov 07 2004

Status

approved