A193866 Even pentagonal numbers divided by 2.
0, 6, 11, 35, 46, 88, 105, 165, 188, 266, 295, 391, 426, 540, 581, 713, 760, 910, 963, 1131, 1190, 1376, 1441, 1645, 1716, 1938, 2015, 2255, 2338, 2596, 2685, 2961, 3056, 3350, 3451, 3763, 3870, 4200, 4313, 4661, 4780, 5146, 5271, 5655, 5786, 6188
Offset: 0
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
Programs
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Magma
[1/16*(1-3*(-1)^n+12*n)*(1-(-1)^n+4*n): n in [0..60]]; // Vincenzo Librandi, Jun 20 2015
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Mathematica
Table[(1/16 (1 - 3 (-1)^n + 12 n) (1 - (-1)^n + 4 n)), {n, 0, 50}] (* Vincenzo Librandi, Jun 20 2015 *) Select[PolygonalNumber[5,Range[0,100]],EvenQ]/2 (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 13 2018 *) -
PARI
a(n)=3*n^2+if(n%2,5*n+1,-n)/2 \\ Charles R Greathouse IV, Aug 18 2011
Formula
a(n) = 1/16*(1-3*(-1)^n+12*n)*(1-(-1)^n+4*n).
a(n) = A014633(n)/2.
a(0)=0, a(1)=6, a(2)=11, a(3)=35, a(4)=46, a(n)=a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5). G.f.: x*(6+5*x+12*x^2+x^3)/(1-x-2*x^2+2*x^3+x^4-x^5). [Colin Barker, Jan 25 2012]