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A253879 Indices of centered heptagonal numbers (A069099) which are also triangular numbers (A000217). 3

%I

%S 1,9,136,2160,34417,548505,8741656,139317984,2220346081,35386219305,

%T 563959162792,8987960385360,143243407002961,2282906551662009,

%U 36383261419589176,579849276161764800,9241205157168647617,147279433238536597065,2347229726659416905416

%N Indices of centered heptagonal numbers (A069099) which are also triangular numbers (A000217).

%C Also positive integers y in the solutions to x^2 - 7*y^2 + x + 7*y - 2 = 0, the corresponding values of x being A253878.

%H Colin Barker, <a href="/A253879/b253879.txt">Table of n, a(n) for n = 1..832</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (17,-17,1).

%F a(n) = 17*a(n-1)-17*a(n-2)+a(n-3).

%F G.f.: x*(8*x-1) / ((x-1)*(x^2-16*x+1)).

%F a(n) = (14-(8-3*sqrt(7))^n*(7+3*sqrt(7))+(-7+3*sqrt(7))*(8+3*sqrt(7))^n)/28. - _Colin Barker_, Mar 04 2016

%e 9 is in the sequence because the 9th centered heptagonal number is 253, which is also the 22nd triangular number.

%o (PARI) Vec(x*(8*x-1)/((x-1)*(x^2-16*x+1)) + O(x^100))

%Y Cf. A000217, A069099, A253878, A253880.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Jan 17 2015

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Last modified March 7 13:24 EST 2021. Contains 341886 sequences. (Running on oeis4.)