A191967 n * (numbers that are not divisible by 3).

0, 1, 4, 12, 20, 35, 48, 70, 88, 117, 140, 176, 204, 247, 280, 330, 368, 425, 468, 532, 580, 651, 704, 782, 840, 925, 988, 1080, 1148, 1247, 1320, 1426, 1504, 1617, 1700, 1820, 1908, 2035, 2128, 2262, 2360, 2501, 2604, 2752, 2860, 3015, 3128, 3290, 3408

Offset

0,3

Comments

A033579 and A033570 interleaved.

Links

Table of n, a(n) for n=0..48.

Eric Weisstein's World of Mathematics, Pentagonal Number.

Wikipedia, Pentagonal number.

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Formula

a(n) = n * A001651(n).

a(n) = A000326(n) - A142150(n).

a(2*n) = A033579(n) = 4 * A000326(n);

a(2*n+1) = A033570(n) = A000326(2*n+1).

G.f.: x*(1+3*x+6*x^2+2*x^3)/((1+x)^2*(1-x)^3). - Bruno Berselli, Jul 09 2012

a(n) = A182079(3n). - Bruno Berselli, Jul 09 2012

From Amiram Eldar, Feb 18 2022: (Start)

Sum_{n>=1} 1/a(n) = Pi/(4*sqrt(3)) + 9*log(3)/4 - 2*log(2).

Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(3)*Pi/4 + 3*log(3)/4 - 2*log(2). (End)

Mathematica

Table[n (6 n - 3 - (-1)^n)/4, {n, 0, 48}] (* Bruno Berselli, Jul 09 2012 *)

Prog

(Haskell)
a191967 n = n * a001651 n
(Magma) A001651:=func<n|(6*n-3-(-1)^n)/4>; [n*A001651(n): n in [0..48]]; // Bruno Berselli, Jul 09 2012
(PARI) a(n)=n\2*3*n+if(n%2, n, -n) \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A000326, A001651, A033570, A033579, A142150, A182079.

Sequence in context: A038438 A008207 A008101 * A016439 A008108 A301004

Adjacent sequences: A191964 A191965 A191966 * A191968 A191969 A191970

Keyword

nonn,easy

Author

Reinhard Zumkeller, Jul 07 2012

Status

approved