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A253447 Indices of centered octagonal numbers (A016754) which are also centered heptagonal numbers (A069099). 3
1, 15, 435, 13021, 390181, 11692395, 350381655, 10499757241, 314642335561, 9428770309575, 282548466951675, 8467025238240661, 253728208680268141, 7603379235169803555, 227847648846413838495, 6827826086157245351281, 204606934935870946699921 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also positive integers y in the solutions to 7*x^2 - 8*y^2 - 7*x + 8*y = 0, the corresponding values of x being A253446.

LINKS

Colin Barker, Table of n, a(n) for n = 1..678

Giovanni Lucca, Circle Chains Inscribed in Symmetrical Lenses and Integer Sequences, Forum Geometricorum, Volume 16 (2016) 419-427.

Index entries for linear recurrences with constant coefficients, signature (31,-31,1).

FORMULA

a(n) = 31*a(n-1)-31*a(n-2)+a(n-3).

G.f.: -x*(x^2-16*x+1) / ((x-1)*(x^2-30*x+1)).

a(n) = (8+(4+sqrt(14))*(15+4*sqrt(14))^(-n)-(-4+sqrt(14))*(15+4*sqrt(14))^n)/16. - Colin Barker, Mar 03 2016

EXAMPLE

15 is in the sequence because the 15th centered octagonal number is 841, which is also the 16th centered heptagonal number.

PROG

(PARI) Vec(-x*(x^2-16*x+1)/((x-1)*(x^2-30*x+1)) + O(x^100))

CROSSREFS

Cf. A016754, A069099, A253446, A253514.

Sequence in context: A069431 A133791 A323781 * A302112 A262077 A225492

Adjacent sequences:  A253444 A253445 A253446 * A253448 A253449 A253450

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Jan 01 2015

STATUS

approved

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Last modified July 25 03:53 EDT 2021. Contains 346283 sequences. (Running on oeis4.)