The On-Line Encyclopedia of Integer Sequences (OEIS)

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A203628

Indices of 9-gonal (nonagonal) numbers which are also 10-gonal (decagonal).
(history; published version)

#10 by Ray Chandler at Sat Aug 01 10:03:21 EDT 2015

STATUS

editing

approved

#9 by Ray Chandler at Sat Aug 01 10:03:16 EDT 2015

LINKS

<a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (899, -899, 1).

STATUS

approved

editing

#8 by Bruno Berselli at Sun Sep 15 02:01:36 EDT 2013

STATUS

proposed

approved

#7 by Jon E. Schoenfield at Sun Sep 15 01:16:05 EDT 2013

STATUS

editing

proposed

#6 by Jon E. Schoenfield at Sun Sep 15 01:16:03 EDT 2013

NAME

Indices of 9-gonal (nonagonal ) numbers which are also 10-gonal (decagonal).

EXAMPLE

The second number that is both 9-gonal (nonagonal ) and 10-gonal (decagonal ) is A001106(589) = 1212751. Hence a(2) = 589.

CROSSREFS

Cf. A203627, A203629, A001107, A001106.

STATUS

approved

editing

#5 by Russ Cox at Fri Mar 30 18:41:06 EDT 2012

AUTHOR

_Ant King (mathstutoring(AT)ntlworld.com), _, Jan 06 2012

Discussion

Fri Mar 30

18:41

OEIS Server: https://oeis.org/edit/global/231

#4 by Bruno Berselli at Sat Jan 07 11:01:31 EST 2012

STATUS

proposed

approved

#3 by Ant King at Fri Jan 06 12:36:22 EST 2012

STATUS

editing

proposed

#2 by Ant King at Fri Jan 06 12:36:16 EST 2012

NAME

allocated for Ant KingIndices of nonagonal numbers which are also decagonal.

DATA

1, 589, 528601, 474682789, 426264615601, 382785150126589, 343740638549061001, 308678710631906651989, 277193138406813624424801, 248919129610608002826818989, 223529101197187579724859027001, 200728883955944835984920579427589

OFFSET

1,2

COMMENTS

As n increases, this sequence is approximately geometric with common ratio r = lim(n->Infinity, a(n)/a(n-1)) = (2*sqrt(2)+sqrt(7))^4 = 449+120*sqrt(14).

FORMULA

G.f.: x*(1-310*x-11*x^2) / ((1-x)*(1-898*x+x^2)).

a(n) = 898*a(n-1)-a(n-2)-320.

a(n) = 899*a(n-1)-899*a(n-2)+a(n-3).

a(n) = 1/56*((sqrt(2)+2*sqrt(7))*(2*sqrt(2)+sqrt(7))^(4*n-3)+(sqrt(2)-2*sqrt(7))*(2*sqrt(2)-sqrt(7))^(4*n-3)+20).

a(n) = ceiling(1/56*(sqrt(2)+2*sqrt(7))*(2*sqrt(2)+sqrt(7))^(4*n-3)).

EXAMPLE

The second number that is both nonagonal and decagonal is A001106(589) = 1212751. Hence a(2) = 589.

MATHEMATICA

LinearRecurrence[{899, -899, 1}, {1, 589, 528601}, 12]

CROSSREFS

Cf. A203627, A203629, A001107, A001106.

KEYWORD

allocated

nonn,easy

AUTHOR

Ant King (mathstutoring(AT)ntlworld.com), Jan 06 2012

STATUS

approved

editing

#1 by Ant King at Wed Jan 04 06:40:09 EST 2012

NAME

allocated for Ant King

KEYWORD

allocated

STATUS

approved