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A179805 a(0) = 1, a(1) = 3, a(2) = 6 and a(n) = 2*a(n-1) - a(n-2) for n > 3. 2
1, 3, 6, 15, 24, 33, 42, 51, 60, 69, 78, 87, 96, 105, 114, 123, 132, 141, 150, 159, 168, 177, 186, 195, 204, 213, 222, 231, 240, 249, 258, 267, 276, 285, 294, 303, 312, 321, 330, 339, 348, 357, 366, 375, 384, 393, 402 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Apart from the second term, the same as A122709. - R. J. Mathar, Jul 30 2010

For n > 1, a(n) is the maximum value of the sum of the vertices in a normal magic triangle of order n (see formula 10 in Trotter). - Stefano Spezia, Mar 03 2021

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Terrel Trotter, Normal Magic Triangles of Order n, Journal of Recreational Mathematics Vol. 5, No. 1, 1972, pp. 28-32.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

FORMULA

(1 + 3*x + 6*x^2 + 15*x^3 + ...) = (1 + 3*x^2 + 3*x^3 + 3*x^4 + ...) * (1 + 3*x + 3*x^2 + 3*x^3 + 3*x^4 + ...).

a(0) = 1, a(1) = 3, a(2) = 6 and a(n) = 2*a(n-1) - a(n-2) for n > 3.

a(n) = a(n-1) + 9 for n > 2.

For n > 1, a(n) == 6 (mod 9).

From Colin Barker, Oct 28 2012: (Start)

a(n) = 9*n - 12 for n > 1.

G.f.: (2*x+1)*(3*x^2-x+1)/(x-1)^2. (End)

E.g.f.: 13 + 6*x + 3*exp(x)*(3x - 4). - Stefano Spezia, Mar 03 2021

EXAMPLE

a(4) = 24 = 9 + a(3) = 9 + 15.

a(4) = 24 = 2*a(3) - a(2) = 2*15 - 6.

MATHEMATICA

LinearRecurrence[{2, -1}, {1, 3, 6, 15}, 50] (* Harvey P. Dale, Sep 25 2018 *)

CROSSREFS

Cf. A122709.

Sequence in context: A244164 A129602 A044888 * A006639 A242757 A166448

Adjacent sequences:  A179802 A179803 A179804 * A179806 A179807 A179808

KEYWORD

nonn,easy,changed

AUTHOR

Gary W. Adamson, Jul 27 2010

STATUS

approved

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Last modified March 9 03:05 EST 2021. Contains 341961 sequences. (Running on oeis4.)