A194275 Concentric pentagonal numbers of the second kind: a(n) = floor(5*n*(n+1)/6).
0, 1, 5, 10, 16, 25, 35, 46, 60, 75, 91, 110, 130, 151, 175, 200, 226, 255, 285, 316, 350, 385, 421, 460, 500, 541, 585, 630, 676, 725, 775, 826, 880, 935, 991, 1050, 1110, 1171, 1235, 1300, 1366, 1435, 1505, 1576, 1650, 1725, 1801, 1880, 1960, 2041, 2125
Offset: 0
Examples
Using the numbers A008706 we can write: 0, 1, 5, 10, 15, 20, 25, 30, 35, 40, 45, ... 0, 0, 0, 0, 1, 5, 10, 15, 20, 25, 30, ... 0, 0, 0, 0, 0, 0, 0, 1, 5, 10, 15, ... 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, ... And so on. =========================================== The sums of the columns give this sequence: 0, 1, 5, 10, 16, 25, 35, 46, 60, 75, 91, ... ... Illustration of initial terms (in a precise representation the pentagons should appear strictly concentric): . o . o o . o o o . o o o o o . o o o o o o o . o o o o o o o o o . o o o o o o o . o o o o o o o o . o o o o o o o o o o o o o o o . . 1 5 10 16 25
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).
Crossrefs
Programs
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Magma
[Floor(5*n*(n+1)/6): n in [0..60]]; // Vincenzo Librandi, Sep 27 2011
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Mathematica
Table[Floor[5 n (n + 1)/6], {n, 0, 50}] (* Arkadiusz Wesolowski, Oct 03 2011 *) -
PARI
a(n)=5*n*(n+1)\6 \\ Charles R Greathouse IV, Aug 23 2011
Formula
G.f.: (-1 - 3*x - x^2)/((-1 + x)^3*(1 + x + x^2)). - Alexander R. Povolotsky, Aug 22 2011
a(n) = floor(5*n*(n+1)/6). - Arkadiusz Wesolowski, Aug 23 2011
Extensions
Name improved by Arkadiusz Wesolowski, Aug 23 2011
New name from Omar E. Pol, Sep 28 2011
Comments