cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A280113 Triangular numbers (A000217) that are also centered 10-gonal numbers (A062786).

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%I A280113 #11 Dec 29 2017 20:24:13
%S A280113 1,1711,2467531,3558178261,5130890585101,7398740665537651,
%T A280113 10668978908814707911,15384660187770143270281,
%U A280113 22184669321785637781037561,31990277777354701910112892951,46129958370276158368745010598051,66519367979660443013028395169496861
%N A280113 Triangular numbers (A000217) that are also centered 10-gonal numbers (A062786).
%H A280113 Colin Barker, <a href="/A280113/b280113.txt">Table of n, a(n) for n = 1..300</a>
%H A280113 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1443,-1443,1).
%F A280113 a(n) = 1443*a(n-1) - 1443*a(n-2) + a(n-3) for n>3.
%F A280113 G.f.: x*(1 + 268*x + x^2) / ((1 - x)*(1 - 1442*x + x^2)).
%e A280113 1711 is in the sequence because the 58th triangular number is 1711, which is also the 19th centered 10-gonal number.
%t A280113 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 A280113 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 A280113 LinearRecurrence[{1443,-1443,1},{1,1711,2467531},20] (* _Harvey P. Dale_, Dec 29 2017 *)
%o A280113 (PARI) Vec(x*(1 + 268*x + x^2) / ((1 - x)*(1 - 1442*x + x^2)) + O(x^15))
%Y A280113 Cf. A000217, A062786, A280111, A280112.
%K A280113 nonn,easy
%O A280113 1,2
%A A280113 _Colin Barker_, Dec 26 2016