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

Author

Reinhard Zumkeller, Jul 07 2012

Keywords

• nonn
• easy

Comments

A033579 and A033570 interleaved.

Links

• 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).

Crossrefs

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

Programs

Haskell

a191967 n = n * a001651 n

Magma

A001651:=func; [n*A001651(n): n in [0..48]]; // Bruno Berselli, Jul 09 2012

Mathematica

Table[n (6 n - 3 - (-1)^n)/4, {n, 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

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)