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Heptagonal numbers (A000566) which are also centered triangular numbers (A005448).
3

%I #8 Oct 12 2024 17:08:37

%S 1,235,2839,902101,10906669,3465871039,41903418691,13315875628969,

%T 160992923703385,51159590700627091,618534770964985711,

%U 196555134155933653885,2376410429054551397509,755164774267506397598311,9130168249892815504243099,2901342866180625423639056209

%N Heptagonal numbers (A000566) which are also centered triangular numbers (A005448).

%H Colin Barker, <a href="/A254676/b254676.txt">Table of n, a(n) for n = 1..558</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,3842,-3842,-1,1).

%F a(n) = a(n-1)+3842*a(n-2)-3842*a(n-3)-a(n-4)+a(n-5).

%F G.f.: -x*(x^4+234*x^3-1238*x^2+234*x+1) / ((x-1)*(x^2-62*x+1)*(x^2+62*x+1)).

%e 235 is in the sequence because it is the 10th heptagonal number and the 13th centered triangular number.

%t LinearRecurrence[{1,3842,-3842,-1,1},{1,235,2839,902101,10906669},20] (* _Harvey P. Dale_, Oct 12 2024 *)

%o (PARI) Vec(-x*(x^4+234*x^3-1238*x^2+234*x+1)/((x-1)*(x^2-62*x+1)*(x^2+62*x+1)) + O(x^100))

%Y Cf. A000566, A005448, A254674, A254675.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Feb 05 2015