login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A195019 Multiples of 3 and of 4 interleaved: a(2*n-1) = 3*n, a(2*n) = 4*n. 24
3, 4, 6, 8, 9, 12, 12, 16, 15, 20, 18, 24, 21, 28, 24, 32, 27, 36, 30, 40, 33, 44, 36, 48, 39, 52, 42, 56, 45, 60, 48, 64, 51, 68, 54, 72, 57, 76, 60, 80, 63, 84, 66, 88, 69, 92, 72, 96, 75, 100, 78, 104, 81, 108, 84, 112, 87, 116, 90, 120, 93, 124, 96, 128 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

First differences of A195020.

a(n) is also the length of the n-th edge of a square spiral in which the first two edges are the legs of the primitive Pythagorean triple [3, 4, 5]. The spiral contains infinitely many Pythagorean triples in which the hypotenuses are the positives A008587. Zero together with partial sums give A195020; the vertices of the spiral.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Ron Knott, Pythagorean triangles and triples

Eric Weisstein's World of Mathematics, Pythagorean Triple

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

FORMULA

pair(3*n, 4*n).

a(2*n-1) = 3*n, a(2*n) = 4*n. - M. F. Hasler, Sep 08 2011

G.f.: x*(3+4*x) / ( (x-1)^2*(1+x)^2 ). - R. J. Mathar, Sep 09 2011

From Bruno Berselli, Sep 12 2011: (Start)

a(n) = ((n-3)*(-1)^n + 7*n + 3)/4.

a(n) + a(n+1) = A047355(n+2). (End)

E.g.f.: (1/4)*((3 + 7*x)*exp(x) - (3 + x)*exp(-x)). - G. C. Greubel, Aug 19 2017

MATHEMATICA

Table[((n-3)*(-1)^n + 7*n + 3)/4, {n, 1, 50}] (* G. C. Greubel, Aug 19 2017 *)

PROG

(PARI) a(n)=(n+1)\2*(4-n%2)  \\ M. F. Hasler, Sep 08 2011

(MAGMA) [((n-3)*(-1)^n+7*n+3)/4: n in [1..60]]; // Vincenzo Librandi, Sep 12 2011

CROSSREFS

Cf. A008585, A008586, A026741, A195020-A195029, A195031, A195033, A195035.

Sequence in context: A192284 A024324 A255773 * A288601 A192519 A036446

Adjacent sequences:  A195016 A195017 A195018 * A195020 A195021 A195022

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Sep 07 2011, Sep 12 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 17 17:27 EST 2018. Contains 299296 sequences. (Running on oeis4.)