A133272 - OEIS

%I #24 Jan 07 2024 15:10:50

%S 1,7,78,924,11005,131131,1562562,18619608,221872729,2643853135,

%T 31504364886,375408525492,4473397941013,53305366766659,

%U 635191003258890,7568986672340016,90192649064821297,1074742802105515543

%N Indices of centered heptagonal numbers (A069099) which are also heptagonal numbers (A000566).

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

%C 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

%C Also indices of centered pentagonal numbers (A005891) which are also centered heptagonal numbers (A069099). - _Colin Barker_, Jan 06 2015

%H Colin Barker, <a href="/A133272/b133272.txt">Table of n, a(n) for n = 1..930</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (13,-13,1).

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

%F a(n+1) = 6*a(n) - 5/2 + (1/2)*sqrt(140*a(n)^2 - 140*a(n) + 49).

%F G.f.: x*(-1+6*x)/((-1+x)*(1-12*x+x^2)). - _R. J. Mathar_, Nov 14 2007

%F a(n) = 13*a(n-1) - 13*a(n-2) + a(n-3). - _Colin Barker_, Jan 06 2015

%t LinearRecurrence[{13,-13,1},{1,7,78},25] (* _Paolo Xausa_, Jan 07 2024 *)

%o (PARI) Vec(x*(6*x-1)/((x-1)*(x^2-12*x+1)) + O(x^100)) \\ _Colin Barker_, Jan 06 2015

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

%K nonn,easy

%O 1,2

%A _Richard Choulet_, Oct 16 2007

%E More terms from _Paolo P. Lava_, Jul 14 2008