A129428 Centered 47-gonal numbers.
1, 48, 142, 283, 471, 706, 988, 1317, 1693, 2116, 2586, 3103, 3667, 4278, 4936, 5641, 6393, 7192, 8038, 8931, 9871, 10858, 11892, 12973, 14101, 15276, 16498, 17767, 19083, 20446, 21856, 23313, 24817, 26368, 27966, 29611, 31303, 33042, 34828, 36661, 38541
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Magma
[1+(47/2)*n+(47/2)*n^2: n in [0..50]]; // Vincenzo Librandi, Sep 09 2016
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Mathematica
LinearRecurrence[{3, -3, 1}, {1, 48, 142}, 70] (* Vincenzo Librandi, Sep 09 2016 *) -
PARI
a(n)=47*n*(n+1)/2+1 \\ Charles R Greathouse IV, Jun 17 2017
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SageMath
[1+47*binomial(n+1,2) for n in range(51)] # G. C. Greubel, Feb 05 2024
Formula
a(n) = (1/2)*(2 + 47*n + 47*n^2).
From Colin Barker, Jul 27 2013: (Start)
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
G.f.: (1 + 45*x + x^2)/(1-x)^3. (End)
E.g.f.: (1/2)*(2 + 94*x + 47*x^2)*exp(x). - G. C. Greubel, Feb 05 2024