A028993 Odd 10-gonal (or decagonal) numbers.
1, 27, 85, 175, 297, 451, 637, 855, 1105, 1387, 1701, 2047, 2425, 2835, 3277, 3751, 4257, 4795, 5365, 5967, 6601, 7267, 7965, 8695, 9457, 10251, 11077, 11935, 12825, 13747, 14701, 15687, 16705, 17755, 18837, 19951, 21097, 22275, 23485, 24727, 26001, 27307, 28645
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Eric Weisstein's World of Mathematics, Decagonal Number.
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Magma
[(2*n+1)*(8*n+1): n in [0..60]]; // Vincenzo Librandi, Oct 18 2013
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Maple
A028993:=n->(2*n+1)*(8*n+1): seq(A028993(n), n=0..100); # Wesley Ivan Hurt, Apr 26 2017
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Mathematica
CoefficientList[Series[-(7 x^2 + 24 x + 1)/(x - 1)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Oct 18 2013 *) Select[PolygonalNumber[10,Range[100]],OddQ] (* or *) LinearRecurrence[{3,-3,1},{1,27,85},50] (* Harvey P. Dale, May 03 2023 *) -
PARI
a(n)=(2*n+1)*(8*n+1) \\ Charles R Greathouse IV, Oct 07 2015
Formula
a(n) = (2*n+1)*(8*n+1). - N. J. A. Sloane
G.f.: -(7*x^2+24*x+1)/(x-1)^3. - Colin Barker, Nov 18 2012
Sum_{n>=0} 1/a(n) = (4*log(2) + (sqrt(2)+1)*Pi + 2*sqrt(2)*log(1+sqrt(2)))/12. - Amiram Eldar, Feb 27 2022
From Elmo R. Oliveira, Oct 27 2024: (Start)
E.g.f.: exp(x)*(1 + 26*x + 16*x^2).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)