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A133272 Indices of centered heptagonal numbers (A069099) which are also heptagonal numbers (A000566). 3
1, 7, 78, 924, 11005, 131131, 1562562, 18619608, 221872729, 2643853135, 31504364886, 375408525492, 4473397941013, 53305366766659, 635191003258890, 7568986672340016, 90192649064821297, 1074742802105515543 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers X such that 140*X^2-140*X+49 is a square.

Also positive integers x in the solutions to 5*x^2 - 7*y^2 - 5*x + 7*y = 0, the corresponding values of y being A253621. - Colin Barker, Jan 06 2015

Also indices of centered pentagonal numbers (A005891) which are also centered heptagonal numbers (A069099). - Colin Barker, Jan 06 2015

LINKS

Colin Barker, Table of n, a(n) for n = 1..930

Index entries for linear recurrences with constant coefficients, signature (13,-13,1).

FORMULA

a(n+2) = 12*a(n+1)-a(n)-5.

a(n+1) = 6*a(n)-2.5+0.5*(140*a(n)^2-140*a(n)+49)^0.5.

G.f.: x*(-1+6*x)/(-1+x)/(1-12*x+x^2). - R. J. Mathar, Nov 14 2007

a(n) = (1/2)+(1/4)*[6-sqrt(35)]^(n-1)+(1/20)*sqrt(35)*[6+sqrt(35)]^(n-1)+(1/4)*[6+sqrt(35)]^(n-1)-(1/20)*[6 -sqrt(35)]^(n-1)*sqrt(35), with n>=1 - Paolo P. Lava, Jul 14 2008

a(n) = 13*a(n-1)-13*a(n-2)+a(n-3). - Colin Barker, Jan 06 2015

PROG

(PARI) Vec(x*(6*x-1)/((x-1)*(x^2-12*x+1)) + O(x^100)) \\ Colin Barker, Jan 06 2015

CROSSREFS

Cf. A000566, A069099, A128919, A253621, A253622.

Sequence in context: A045485 A068621 A210406 * A186657 A079590 A202755

Adjacent sequences:  A133269 A133270 A133271 * A133273 A133274 A133275

KEYWORD

nonn,easy

AUTHOR

Richard Choulet, Oct 16 2007

EXTENSIONS

More terms from Paolo P. Lava, Jul 14 2008

STATUS

approved

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Last modified October 18 00:09 EDT 2019. Contains 328135 sequences. (Running on oeis4.)