%I #35 Dec 02 2018 11:57:33

%S 3,7,17,33,55,83,117,157,203,255,313,377,447,523,605,693,787,887,993,

%T 1105,1223,1347,1477,1613,1755,1903,2057,2217,2383,2555,2733,2917,

%U 3107,3303,3505,3713,3927,4147,4373,4605,4843,5087,5337,5593,5855,6123,6397,6677,6963,7255,7553,7857

%N a(n) = 3*n^2 + n + 3.

%C Numbers represented as the palindrome 313 in number base n including base n=1, base 2 (binary) and base 3 with 'illegal' digit 3: 313_1=7, 313_2=17, 313_3=33, ... 313_9=255, 313_10=313, ...

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1).

%F a(n) = A131649(n+3) + 1, n >= 2 (conjectured).

%F a(n) = A056108(n) + 2 = A049451(n) + 3 = A144391(n) + 4.

%e 313 in base 7 is 3*7^2 + 1*7 + 3 = 157.

%t Array[3 #^2 + # + 3 &, 52, 0] (* _Michael De Vlieger_, Nov 15 2017 *)

%t LinearRecurrence[{3, -3, 1}, {3, 7, 17}, 52] (* or *)

%t CoefficientList[Series[-(5 x^2 - 2 x + 3)/(x - 1)^3, {x, 0, 51}], x] (* _Robert G. Wilson v_, Nov 29 2017 *)

%o (PARI) a(n) = 3*n^2 + n + 3; \\ _Michel Marcus_, Dec 15 2017

%Y Cf. A049451, A056108, A131649, A144391.

%K nonn,easy

%O 0,1

%A _Ron Knott_, Nov 14 2017