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A193866 Even pentagonal numbers divided by 2. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 24 09:40 EST 2020. Contains 332209 sequences. (Running on oeis4.)