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
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).
Programs
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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 *) -
PARI
a(n)=15*n^2/4+11*((-1)^n-1)/8 \\ Charles R Greathouse IV, Oct 07 2015
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
Extensions
a(1)=1 added by Harvey P. Dale, Feb 23 2012