A195046 Concentric 15-gonal numbers.

0, 1, 15, 31, 60, 91, 135, 181, 240, 301, 375, 451, 540, 631, 735, 841, 960, 1081, 1215, 1351, 1500, 1651, 1815, 1981, 2160, 2341, 2535, 2731, 2940, 3151, 3375, 3601, 3840, 4081, 4335, 4591, 4860, 5131, 5415, 5701, 6000, 6301, 6615, 6931, 7260, 7591

Offset

0,3

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Formula

a(n) = 15*n^2/4+11*((-1)^n-1)/8.

From Harvey P. Dale, Feb 23 2012: (Start)

a(0)=0, a(1)=1, a(2)=15, a(3)=31, a(n)=2*a(n-1)-2*a(n-3)+a(n-4).

G.f.: -((x*(1+x*(13+x)))/((-1+x)^3*(1+x))). (End)

Sum_{n>=1} 1/a(n) = Pi^2/90 + tan(sqrt(11/15)*Pi/2)*Pi/sqrt(165). - Amiram Eldar, Jan 16 2023

Mathematica

Table[15n^2/4+11((-1)^n-1)/8, {n, 0, 50}] (* or *) LinearRecurrence[ {2, 0, -2, 1}, {0, 1, 15, 31}, 50] (* Harvey P. Dale, Feb 23 2012 *)

Prog

(PARI) a(n)=15*n^2/4+11*((-1)^n-1)/8 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Column 15 of A195040.

Cf. A032527, A032528, A195045, A195047, A195145, A195146.

Sequence in context: A132757 A045135 A283122 * A324631 A346897 A102955

Adjacent sequences: A195043 A195044 A195045 * A195047 A195048 A195049

Keyword

nonn,easy

Author

Omar E. Pol, Sep 27 2011

Extensions

a(1)=1 added by Harvey P. Dale, Feb 23 2012

Status

approved