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Octagonal numbers (A000567) that are also centered heptagonal numbers (A069099).
3

%I #8 Jun 13 2015 00:55:24

%S 1,8,736,5461,496133,3680776,334392976,2480837633,225380369761,

%T 1672080883936,151906034826008,1126980034935301,102384442092359701,

%U 759582871465509008,69006962064215612536,511957728387718136161,46510590046839230489633,345058749350450558263576

%N Octagonal numbers (A000567) that are also centered heptagonal numbers (A069099).

%H Colin Barker, <a href="/A254857/b254857.txt">Table of n, a(n) for n = 1..708</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,674,-674,-1,1).

%F a(n) = a(n-1)+674*a(n-2)-674*a(n-3)-a(n-4)+a(n-5).

%F G.f.: -x*(x^4+7*x^3+54*x^2+7*x+1) / ((x-1)*(x^2-26*x+1)*(x^2+26*x+1)).

%e 736 is in the sequence because it is the 16th octagonal number and the 15th centered heptagonal number.

%o (PARI) Vec(-x*(x^4+7*x^3+54*x^2+7*x+1)/((x-1)*(x^2-26*x+1)*(x^2+26*x+1)) + O(x^100))

%Y Cf. A000567, A069099, A254855, A254856.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Feb 08 2015