A253923 - OEIS

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

%S 1,7701,219781,1789106881,51059956641,415648888795141,

%T 11862351246525781,96564381140875635681,2755885166244302532001,

%U 22434030154994860543881301,640252753580346501593005701,5211918753572151610134715970401,148744800214537374776845967930881

%N Octagonal numbers (A000567) which are also centered pentagonal numbers (A005891).

%H Colin Barker, <a href="/A253923/b253923.txt">Table of n, a(n) for n = 1..373</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,232322,-232322,-1,1).

%F a(n) = a(n-1)+232322*a(n-2)-232322*a(n-3)-a(n-4)+a(n-5).

%F G.f.: -x*(x^4+7700*x^3-20242*x^2+7700*x+1) / ((x-1)*(x^2-482*x+1)*(x^2+482*x+1)).

%e 7701 is in the sequence because it is the 51st octagonal number and the 56th centered pentagonal number.

%t CoefficientList[Series[(x^4 + 7700 x^3 - 20242 x^2 + 7700 x + 1) / ((1 - x) (x^2 - 482 x + 1) (x^2 + 482 x + 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jan 20 2015 *)

%o (PARI) Vec(-x*(x^4+7700*x^3-20242*x^2+7700*x+1)/((x-1)*(x^2-482*x+1)*(x^2+482*x+1)) + O(x^100))

%o (Magma) I:=[1,7701,219781,1789106881,51059956641]; [n le 5 select I[n] else Self(n-1)+232322*Self(n-2)-232322*Self(n-3)-Self(n-4)+Self(n-5): n in [1..25]]; // _Vincenzo Librandi_, Jan 20 2015

%Y Cf. A000567, A005891, A253921, A253922.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Jan 19 2015