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A262402 Number of triangles on a 3 X n grid. 1
0, 18, 76, 200, 414, 742, 1208, 1836, 2650, 3674, 4932, 6448, 8246, 10350, 12784, 15572, 18738, 22306, 26300, 30744, 35662, 41078, 47016, 53500, 60554, 68202, 76468, 85376, 94950, 105214, 116192, 127908, 140386, 153650, 167724, 182632, 198398, 215046, 232600 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Peter Kagey, Table of n, a(n) for n = 1..10000

Ran Pan, Exercise T, Project P

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

FORMULA

a(n) = 4*n^3 - 3*n^2 - 3*n + 4, n>=2.

G.f.: -2 * (x^3-2*x^2-2*x-9) * x^2 / (x-1)^4.

MATHEMATICA

CoefficientList[Series[- 2 x (x^3 - 2 x^2 - 2 x - 9)/(x - 1)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Sep 23 2015 *)

Join[{0}, LinearRecurrence[{4, -6, 4, -1}, {18, 76, 200, 414}, 38]] (* Ray Chandler, Sep 23 2015 *)

PROG

(MAGMA) [0] cat [4*n^3-3*n^2-3*n+4: n in [2..40]]; // Vincenzo Librandi, Sep 23 2015

CROSSREFS

Sequence in context: A143666 A139757 A285918 * A164603 A229714 A100187

Adjacent sequences:  A262399 A262400 A262401 * A262403 A262404 A262405

KEYWORD

nonn,easy

AUTHOR

Ran Pan, Sep 21 2015

STATUS

approved

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Last modified September 26 06:54 EDT 2017. Contains 292502 sequences.