

A133043


Number of segments needed to draw the spiral of equilateral triangles with side lengths which follow the Padovan sequence.


1



3, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65
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OFFSET

1,1


REFERENCES

Mohammad K. Azarian, A Trigonometric Characterization of Equilateral Triangle, Problem 336, Mathematics and Computer Education, Vol. 31, No. 1, Winter 1997, p. 96. Solution published in Vol. 32, No. 1, Winter 1998, pp. 8485.
Mohammad K. Azarian, Equating Distances and Altitude in an Equilateral Triangle, Problem 316, Mathematics and Computer Education, Vol. 28, No. 3, Fall 1994, p. 337. Solution published in Vol. 29, No. 3, Fall 1995, pp. 324325.


LINKS

Table of n, a(n) for n=1..61.
Index entries for linear recurrences with constant coefficients, signature (2,1).


FORMULA

a(1)=3: a(2)=5: a(3)=6; for n>3, a(n)=n+4.


MATHEMATICA

LinearRecurrence[{2, 1}, {3, 5, 6, 8, 9}, 70] (* Harvey P. Dale, Dec 21 2018 *)


PROG

(PARI) a(n)=if(n>3, n+4, [3, 5, 6][n]) \\ Charles R Greathouse IV, Oct 27 2011


CROSSREFS

Cf. Padovan sequence: A000931.
Sequence in context: A201906 A267158 A161529 * A094058 A288134 A175966
Adjacent sequences: A133040 A133041 A133042 * A133044 A133045 A133046


KEYWORD

easy,nonn


AUTHOR

Omar E. Pol, Nov 04 2007, Nov 05 2007


STATUS

approved



