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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A214345 Interleaved reading of A073577 and A053755. 15
5, 7, 17, 23, 37, 47, 65, 79, 101, 119, 145, 167, 197, 223, 257, 287, 325, 359, 401, 439, 485, 527, 577, 623, 677, 727, 785, 839, 901, 959, 1025, 1087, 1157, 1223, 1297, 1367, 1445, 1519, 1601, 1679, 1765, 1847, 1937, 2023, 2117, 2207, 2305, 2399, 2501 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The elements of this sequence satisfy the property that for every n=2k the triple (a(2k-1)^2, a(2k)^2 , a(2k+1)^2) is an arithmetic progression, i.e., 2*a(2k)^2 = a(2k-1)^2 + a(2k+1)^2. In general a triple((x-y)^2,z^2,(x+y)^2) is an arithmetic progression if and only if x^2+y^2=z^2 : in the case of this sequence 7^2, 17^2, and 23^2 is such a triple (i.e. 15-8 =7, 17, 8+15=23, and 8^2+15^2=17^2) .

The first differences of such a sequence is always an interleaved sequence; in this case the interleaved sequence is 2,10,6,14,10,... (A142954).

LINKS

Guenther Schrack, Table of n, a(n) for n = 0..10001

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

FORMULA

a(2n+1) = A073577(n+1); a(2n) = A053755(n+1).

a(n+1)-a(n) = A142954(n+1).

a(n) = 2*a(n-1)-2*a(n-3)+a(n-4).

G.f.: (x^3-3*x^2+3*x-5)/((x-1)^3*(x+1)).

a(n) = (2*n*(n+4)+3*(-1)^n+7)/2.

2*a(2n)^2 = a(2n-1)^2 + a(2n+1)^2.

a(n) = 4*(n+1) + a(n-2) for n > 1; a(-n) = a(n-4). - Guenther Schrack, Oct 24 2018

EXAMPLE

For n = 7, a(7)=2*a(6)-2*a(4)+a(3)=2*65-2*37+23=79

MAPLE

seq(coeff(series((x^3-3*x^2+3*x-5)/((x-1)^3*(x+1)), x, n+1), x, n), n = 0 .. 50); # Muniru A Asiru, Oct 26 2018

MATHEMATICA

LinearRecurrence[{2, 0, -2, 1}, {5, 7, 17, 23}, 50] (* Harvey P. Dale, Apr 02 2018 *)

PROG

(MAGMA) I:=[5, 7, 17, 23]; [n le 4 select I[n] else 2*Self(n-1)-2*Self(n-3)+Self(n-4): n in [1..75]];

(Maxima) A214345(n):=(2*n*(n+4)+3*(-1)^n+7)/2$

makelist(A214345(n), n, 0, 30); /* Martin Ettl, Nov 01 2012 */

(GAP) a:=[7, 17];; for n in [3..50] do a[n]:=4*(n+1)+a[n-2]; od; Concatenation([5], a); # Muniru A Asiru, Oct 26 2018

CROSSREFS

Cf. A178218.

First differences: A142954; 2-element moving average (a(n-1) + a(n))/2: A002378. - Guenther Schrack, Oct 25 2018

Sequence in context: A283145 A191145 A145354 * A166109 A157755 A265812

Adjacent sequences:  A214342 A214343 A214344 * A214346 A214347 A214348

KEYWORD

nonn,easy

AUTHOR

Yasir Karamelghani Gasmallah, Jul 13 2012

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 15 04:09 EDT 2019. Contains 327062 sequences. (Running on oeis4.)