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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

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OFFSET

0,2

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).

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]

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 *)

PROG

(PARI) a(n)=3*n^2+if(n%2, 5*n+1, -n)/2 \\ Charles R Greathouse IV, Aug 18 2011

(Magma) [1/16*(1-3*(-1)^n+12*n)*(1-(-1)^n+4*n): n in [0..60]]; // Vincenzo Librandi, Jun 20 2015

CROSSREFS

Cf. A000326, A001105, A033991.

Sequence in context: A302177 A186410 A192916 * A152987 A100093 A219500

Adjacent sequences: A193863 A193864 A193865 * A193867 A193868 A193869

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Aug 18 2011

STATUS

approved

URL: https://oeis.org/A193866

⇱ A193866 - OEIS