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A270545 Number of equilateral triangle units forming perimeter of equilateral triangle. 2
1, 4, 9, 15, 21, 27, 33, 39, 45, 51, 57, 63, 69, 75, 81, 87, 93, 99, 105, 111, 117, 123, 129, 135, 141, 147, 153, 159, 165, 171, 177, 183, 189, 195, 201, 207, 213, 219, 225, 231, 237, 243, 249, 255, 261, 267, 273, 279, 285, 291, 297, 303, 309, 315 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This is the triangular equivalent of A008574 (square units forming perimeter of a square).

The height of each triangle is n+1 units.

LINKS

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

Michel Marcus, Illustration of initial terms

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

FORMULA

a(0)=1 and a(1)=4; thereafter a(n) = (n+1)^2-(n-2)^2 = 6*n-3.

a(n) = 2*a(n-1)-a(n-2) for n>3. G.f.: (1+x)*(1+x+x^2) / (1-x)^2. - Colin Barker, Mar 20 2016

a(n) = A016945(n-1), n>1.

MATHEMATICA

CoefficientList[Series[(1 + x) (1 + x + x^2)/(1 - x)^2, {x, 0, 53}], x] (* Michael De Vlieger, Mar 21 2016 *)

PROG

(PARI) a(n)=if(n<2, 3*n+1, 6*n-3) \\ Charles R Greathouse IV, Mar 19 2016

(PARI) Vec((1+x)*(1+x+x^2)/(1-x)^2 + O(x^50)) \\ Colin Barker, Mar 20 2016

CROSSREFS

Cf. A016945, A008574.

Sequence in context: A313295 A313296 A313297 * A358243 A099055 A162801

Adjacent sequences: A270542 A270543 A270544 * A270546 A270547 A270548

KEYWORD

nonn,easy

AUTHOR

Peter M. Chema, Mar 18 2016

STATUS

approved

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Last modified December 6 18:09 EST 2022. Contains 358644 sequences. (Running on oeis4.)