A271779 a(n) = n^3 + 2*n^2 + 5*n + 11.
11, 19, 37, 71, 127, 211, 329, 487, 691, 947, 1261, 1639, 2087, 2611, 3217, 3911, 4699, 5587, 6581, 7687, 8911, 10259, 11737, 13351, 15107, 17011, 19069, 21287, 23671, 26227, 28961, 31879, 34987, 38291, 41797, 45511, 49439, 53587, 57961, 62567, 67411, 72499
Offset: 0
Links
- Roman Witula, Damian Slota and Adam Warzynski, Quasi-Fibonacci Numbers of the Seventh Order, J. Integer Seq., 9 (2006), Article 06.4.3, page 24.
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Magma
[n^3+2*n^2+5*n+11: n in [0..50]];
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Mathematica
Table[n^3 + 2 n^2 + 5 n + 11, {n, 0, 50}] -
PARI
vector(50, n, n--; n^3+2*n^2+5*n+11) \\ Altug Alkan, Apr 14 2016
Formula
O.g.f.: (11 - 25*x + 27*x^2 - 7*x^3)/(1 - x)^4.
E.g.f.: (11 + 8*x + 5*x^2 + x^3)*exp(x).
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3.