A261521 a(n) = n^2 + 2*n + 29.
29, 32, 37, 44, 53, 64, 77, 92, 109, 128, 149, 172, 197, 224, 253, 284, 317, 352, 389, 428, 469, 512, 557, 604, 653, 704, 757, 812, 869, 928, 989, 1052, 1117, 1184, 1253, 1324, 1397, 1472, 1549, 1628, 1709, 1792, 1877, 1964, 2053, 2144, 2237, 2332, 2429, 2528
Offset: 0
Examples
For n = 3, a(3) = 3^2 + 2*3 + 29 = 44.
Links
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Magma
[n^2+2*n+29: n in [0..50]]; // Vincenzo Librandi, Oct 03 2015
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Mathematica
Table[n^2 + 2 n + 29, {n, 0, 50}] (* Bruno Berselli, Oct 25 2015 *) LinearRecurrence[{3,-3,1},{29,32,37},50] (* Harvey P. Dale, Oct 14 2023 *) -
PARI
vector(50, n, n--; n^2+2*n+29) \\ Altug Alkan, Oct 02 2015
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PARI
Vec((29 - 55*x + 28*x^2)/(1-x)^3 + O(x^100)) \\ Altug Alkan, Oct 17 2015
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Python
def a(x):return x*x+2*x+27
Formula
a(n) = a(n-1) + A005408(n), a(0) = 29, for n > 0. - Altug Alkan, Oct 02 2015
From Vincenzo Librandi, Oct 03 2015: (Start)
G.f.: (29 - 55*x + 28*x^2)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
a(n) = A005563(n) + 29. - Omar E. Pol, Oct 17 2015
E.g.f.: (29 + 3*x + x^2)*exp(x). - Elmo R. Oliveira, Oct 19 2024
Comments