A280113 - OEIS

%I #11 Dec 29 2017 20:24:13

%S 1,1711,2467531,3558178261,5130890585101,7398740665537651,

%T 10668978908814707911,15384660187770143270281,

%U 22184669321785637781037561,31990277777354701910112892951,46129958370276158368745010598051,66519367979660443013028395169496861

%N Triangular numbers (A000217) that are also centered 10-gonal numbers (A062786).

%H Colin Barker, <a href="/A280113/b280113.txt">Table of n, a(n) for n = 1..300</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1443,-1443,1).

%F a(n) = 1443*a(n-1) - 1443*a(n-2) + a(n-3) for n>3.

%F G.f.: x*(1 + 268*x + x^2) / ((1 - x)*(1 - 1442*x + x^2)).

%e 1711 is in the sequence because the 58th triangular number is 1711, which is also the 19th centered 10-gonal number.

%t RecurrenceTable[{a[n] == 1443 a[n - 1] - 1443 a[n - 2] + a[n - 3], a[1] == 1, a[2] == 1711, a[3] == 2467531}, a, {n, 12}] (* or *)

%t Rest@ CoefficientList[Series[x (1 + 268 x + x^2)/((1 - x) (1 - 1442 x + x^2)), {x, 0, 12}], x] (* _Michael De Vlieger_, Dec 26 2016 *)

%t LinearRecurrence[{1443,-1443,1},{1,1711,2467531},20] (* _Harvey P. Dale_, Dec 29 2017 *)

%o (PARI) Vec(x*(1 + 268*x + x^2) / ((1 - x)*(1 - 1442*x + x^2)) + O(x^15))

%Y Cf. A000217, A062786, A280111, A280112.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Dec 26 2016