A072025 a(n) = n^4 + 2*n^3 + 4*n^2 + 3*n + 1 = ((n+1)^5+n^5) / (2*n+1).
1, 11, 55, 181, 461, 991, 1891, 3305, 5401, 8371, 12431, 17821, 24805, 33671, 44731, 58321, 74801, 94555, 117991, 145541, 177661, 214831, 257555, 306361, 361801, 424451, 494911, 573805, 661781, 759511, 867691, 987041, 1118305, 1262251, 1419671, 1591381
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Programs
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Magma
[((n+1)^5+n^5)/(2*n+1): n in [0..40]]; // Vincenzo Librandi, Nov 23 2011
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Mathematica
Table[((n+1)^5+n^5)/(2n+1),{n,0,30}] (* Vincenzo Librandi, Nov 23 2011 *) LinearRecurrence[{5,-10,10,-5,1},{1,11,55,181,461},50] (* Harvey P. Dale, Dec 14 2019 *) -
PARI
a(n)=n^4+2*n^3+4*n^2+3*n+1 \\ Charles R Greathouse IV, Nov 23 2011
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PARI
Vec((1+x)^2*(1+4*x+x^2)/(1-x)^5 + O(x^100)) \\ Colin Barker, Dec 01 2015
Formula
From Colin Barker, Dec 01 2015: (Start)
a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5) for n>4.
G.f.: (1+x)^2*(1+4*x+x^2) / (1-x)^5.
(End)