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A036353 Square pentagonal numbers. 6
0, 1, 9801, 94109401, 903638458801, 8676736387298001, 83314021887196947001, 799981229484128697805801, 7681419682192581869134354401, 73756990988431941623299373152801, 708214619789503821274338711878841001, 6800276705461824703444258688161258139001 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

lim(n -> Infinity, a(n)/a(n-1)) = (sqrt(2) + sqrt(3))^8 = 4801 + 1960*sqrt(6). - Ant King, Nov 06 2011

Pentgonal numbers (A000326) which are also centered octagonal numbers (A016754). - Colin Barker, Jan 11 2015

LINKS

Colin Barker, Table of n, a(n) for n = 0..252

Eric Weisstein's World of Mathematics, Pentagonal Square Number

Index entries for linear recurrences with constant coefficients, signature (9603,-9603,1).

FORMULA

a(n) = 9602*a(n-1) - a(n-2) + 200; g.f.: x*(1+198*x+x^2)/((1-x)*(1-9602*x+x^2)). - Warut Roonguthai, Jan 05 2001

a(n+1) = 4801*a(n)+100+980*(24*a(n)^2+a(n))^0.5. - Richard Choulet, Sep 21 2007

From Ant King, Nov 06 2011: (Start)

a(n) = floor(1/96*(sqrt(2) + sqrt(3))^(8n-4)).

a(n) = 9603*a(n-1) - 9603*a(n-2) + a(n-3).

(End)

MATHEMATICA

Table[Floor[1/96 ( Sqrt[2] + Sqrt[3] ) ^ ( 8*n - 4 ) ] , {n, 0, 9}] (* Ant King, Nov 06 2011 *)

PROG

(PARI) for(n=0, 10^9, g=(n*(3*n-1)/2); if(issquare(g), print(g)))

(PARI) concat(0, Vec(x*(1+198*x+x^2)/((1-x)*(1-9602*x+x^2)) + O(x^20))) \\ Colin Barker, Jun 24 2015

CROSSREFS

Cf. A000326, A001078, A001079, A001110, A046172, A046173, A248205.

Sequence in context: A156735 A227489 A113937 * A174769 A031687 A031597

Adjacent sequences:  A036350 A036351 A036352 * A036354 A036355 A036356

KEYWORD

nonn,easy

AUTHOR

Jean-Francois Chariot (jeanfrancois.chariot(AT)afoc.alcatel.fr)

EXTENSIONS

More terms from Eric W. Weisstein

STATUS

approved

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Last modified December 7 05:36 EST 2016. Contains 278841 sequences.