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A280304 a(n) = 3*n*(n^2 + 3*n + 4). 1
0, 24, 84, 198, 384, 660, 1044, 1554, 2208, 3024, 4020, 5214, 6624, 8268, 10164, 12330, 14784, 17544, 20628, 24054, 27840, 32004, 36564, 41538, 46944, 52800, 59124, 65934, 73248, 81084, 89460, 98394, 107904, 118008, 128724, 140070, 152064, 164724, 178068, 192114, 206880, 222384, 238644, 255678, 273504, 292140, 311604, 331914, 353088, 375144, 398100 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Numbers of unit triangles in a certain structure obtained from A006003.

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Luce ETIENNE, Illustration of initial terms

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

FORMULA

G.f.: 6*x*(x^2-2*x+4) / (1-x)^4.

a(n) = 6*(A006003(n+1)-1).

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 3. - Colin Barker, Dec 31 2016

EXAMPLE

a(0) = 6*(1-1) = 0, a(1) = 6*(5-1) = 24, a(2) = 6*(15-1) = 84, a(3) = 6*(34-1) = 198, a(4) = 6*(65-1) = 384.

MAPLE

A280304:=n->3*n*(n^2 + 3*n + 4): seq(A280304(n), n=0..60); # Wesley Ivan Hurt, Dec 31 2016

MATHEMATICA

Table[3 n (n^2 + 3 n + 4), {n, 0, 50}] (* or *)

CoefficientList[Series[6 x (x^2 - 2 x + 4)/(1 - x)^4, {x, 0, 50}], x] (* Michael De Vlieger, Dec 31 2016 *)

PROG

(PARI) concat(0, Vec(6*x*(x^2-2*x+4) / (1-x)^4 + O(x^30))) \\ Colin Barker, Dec 31 2016

(MAGMA) [3*n*(n^2 + 3*n + 4) : n in [0..60]]; // Wesley Ivan Hurt, Dec 31 2016

CROSSREFS

Cf. A003215, A005448, A006003, A033428, A213389, A269064.

Sequence in context: A192838 A289155 A101861 * A168538 A007201 A228874

Adjacent sequences:  A280301 A280302 A280303 * A280305 A280306 A280307

KEYWORD

nonn,easy

AUTHOR

Luce ETIENNE, Dec 31 2016

STATUS

approved

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Last modified December 12 20:12 EST 2019. Contains 329961 sequences. (Running on oeis4.)