A117865
Number of palindromes (in base 6) below 6^n.
Original entry on oeis.org
5, 10, 40, 70, 250, 430, 1510, 2590, 9070, 15550, 54430, 93310, 326590, 559870, 1959550, 3359230, 11757310, 20155390, 70543870, 120932350, 423263230, 725594110, 2539579390, 4353564670, 15237476350, 26121388030, 91424858110, 156728328190, 548549148670
Offset: 1
-
Table[If[OddQ[n], 7*6^((n - 1)/2) - 2, 2*6^(n/2) - 2], {n,25}] (* or *) LinearRecurrence[{1,6,-6},{5, 10, 40},25] (* G. C. Greubel, Oct 27 2016 *)
A117866
Number of palindromes (in base 7) below 7^n.
Original entry on oeis.org
6, 12, 54, 96, 390, 684, 2742, 4800, 19206, 33612, 134454, 235296, 941190, 1647084, 6588342, 11529600, 46118406, 80707212, 322828854, 564950496, 2259801990, 3954653484, 15818613942, 27682574400, 110730297606, 193778020812, 775112083254, 1356446145696
Offset: 1
-
[IsOdd(n) select 8*7^((n-1) div 2)-2 else 2*7^(n div 2)-2: n in [1..30]]; // Vincenzo Librandi, Oct 29 2016
-
Table[If[OddQ[n],8*7^((n-1)/2)-2,2*7^(n/2)-2],{n,30}] (* or *) LinearRecurrence[{1,7,-7},{6,12,54},30] (* Harvey P. Dale, Oct 31 2013 *)
Rest@ CoefficientList[Series[6 x (x + 1)/((x - 1) (7 x^2 - 1)), {x, 0, 28}], x] (* Michael De Vlieger, Oct 31 2016 *)
-
a(n)=([0,1,0; 0,0,1; -7,7,1]^(n-1)*[6;12;54])[1,1] \\ Charles R Greathouse IV, Oct 31 2016
A117867
Number of palindromes (in base 8) below 8^n.
Original entry on oeis.org
7, 14, 70, 126, 574, 1022, 4606, 8190, 36862, 65534, 294910, 524286, 2359294, 4194302, 18874366, 33554430, 150994942, 268435454, 1207959550, 2147483646, 9663676414, 17179869182, 77309411326, 137438953470, 618475290622, 1099511627774, 4947802324990
Offset: 1
-
Table[If[OddQ[n],9*8^((n-1)/2)-2, 2*8^(n/2)-2], {n,1,25}] (* or *) LinearRecurrence[{1,8,-8}, {7,14,70}, 25] (* G. C. Greubel, Oct 27 2016 *)
Rest@ CoefficientList[Series[7 x (x + 1)/((x - 1) (8 x^2 - 1)), {x, 0, 27}], x] (* Michael De Vlieger, Oct 27 2016 *)
A117868
Number of palindromes (in base 9) below 9^n.
Original entry on oeis.org
8, 16, 88, 160, 808, 1456, 7288, 13120, 65608, 118096, 590488, 1062880, 5314408, 9565936, 47829688, 86093440, 430467208, 774840976, 3874204888, 6973568800, 34867844008, 62762119216, 313810596088, 564859072960, 2824295364808, 5083731656656, 25418658283288
Offset: 1
-
seq( 8 * 3^(n-1) + 2 * (-3)^(n-1) - 2, n=1..100); # Robert Israel, Apr 26 2015
-
Table[If[OddQ[n],10*9^((n-1)/2)-2,2*9^(n/2)-2],{n,0,30}] (* or *) LinearRecurrence[ {1,9,-9},{0,8,16},30] (* Harvey P. Dale, Jul 17 2012 *)
-
Vec(8*x*(x+1)/((x-1)*(3*x-1)*(3*x+1)) + O(x^100)) \\ Colin Barker, Apr 26 2015