A253920 - OEIS

%I #13 Sep 08 2022 08:46:11

%S 1,5,39,760,6494,55518,1095199,9363623,80056197,1579275478,

%T 13502337152,115440979836,2277314143357,19470360808841,

%U 166465812866595,3283885415444596,28076246784010850,240043586712649434,4735360491756963355,40485928392182836139

%N Indices of centered octagonal numbers (A016754) which are also heptagonal numbers (A000566).

%C Also positive integers y in the solutions to 5*x^2 - 8*y^2 - 3*x + 8*y - 2 = 0, the corresponding values of x being A046195.

%H Colin Barker, <a href="/A253920/b253920.txt">Table of n, a(n) for n = 1..950</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1442,-1442,0,-1,1).

%F a(n) = a(n-1)+1442*a(n-3)-1442*a(n-4)-a(n-6)+a(n-7).

%F G.f.: x*(4*x^5+34*x^4+721*x^3-34*x^2-4*x-1) / ((x-1)*(x^6-1442*x^3+1)).

%e 5 is in the sequence because the 5th centered octagonal number is 81, which is also the 6th heptagonal number.

%t CoefficientList[Series[(4 x^5 + 34 x^4 + 721 x^3 - 34 x^2 -4 x - 1)/((x-1) (x^6 - 1442 x^3 + 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jan 20 2015 *)

%t LinearRecurrence[{1,0,1442,-1442,0,-1,1},{1,5,39,760,6494,55518,1095199},20] (* _Harvey P. Dale_, Jul 04 2017 *)

%o (PARI) Vec(x*(4*x^5+34*x^4+721*x^3-34*x^2-4*x-1)/((x-1)*(x^6-1442*x^3+1)) + O(x^100))

%o (Magma) I:=[1,5,39,760,6494,55518,1095199]; [n le 7 select I[n] else Self(n-1)+1442*Self(n-3)-1442*Self(n-4)-Self(n-6)+Self(n-7): n in [1..25]]; // _Vincenzo Librandi_, Jan 20 2015

%Y Cf. A000566, A016754, A046195, A036354.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Jan 19 2015

%E Corrected by _Vincenzo Librandi_, Jan 20 2015