login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A129428
Centered 47-gonal numbers.
1
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
0,2
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
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {1, 48, 142}, 70] (* Vincenzo Librandi, Sep 09 2016 *)
PROG
(Magma) [1+(47/2)*n+(47/2)*n^2: n in [0..50]]; // Vincenzo Librandi, Sep 09 2016
(PARI) a(n)=47*n*(n+1)/2+1 \\ Charles R Greathouse IV, Jun 17 2017
(SageMath) [1+47*binomial(n+1, 2) for n in range(51)] # G. C. Greubel, Feb 05 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Oct 06 2007, based on a suggestion from an unknown correspondent in 2004.
STATUS
approved