A061600 a(n) = n^3 - n + 1.
1, 1, 7, 25, 61, 121, 211, 337, 505, 721, 991, 1321, 1717, 2185, 2731, 3361, 4081, 4897, 5815, 6841, 7981, 9241, 10627, 12145, 13801, 15601, 17551, 19657, 21925, 24361, 26971, 29761, 32737, 35905, 39271, 42841, 46621, 50617, 54835, 59281, 63961
Offset: 0
Examples
a(5) = 121 = 5^3 - 5 + 1. We have 121 + 123 + 125 + 127 + 129 = 625 = 5^4.
References
- T. A. Gulliver, Sequences from Cubes of Integers, Int. Math. Journal, 4 (2003), 439-445.
Links
- Harry J. Smith, Table of n, a(n) for n = 0..1000
- Leo Tavares, Illustration: Diamond Chains
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Crossrefs
Cf. A126420.
Programs
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Magma
[n^3 - n + 1: n in [0..40]]; // Vincenzo Librandi, Aug 29 2011
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Mathematica
Table[n^3 - n + 1, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2012 *) LinearRecurrence[{4,-6,4,-1},{1,1,7,25},50] (* Harvey P. Dale, Aug 17 2020 *) -
PARI
a(n) = n^3 - n + 1; \\ Harry J. Smith, Jul 25 2009
Formula
G.f.: (1-3*x+9*x^2-x^3)/(1 - x)^4. a(-n) = -A126420(n). - Bruno Berselli, Aug 29 2011
a(n) = 1 + Sum_{k=1..n} 3*(k-1)*k. - Luce ETIENNE and Michel Marcus, Nov 01 2014
E.g.f.: exp(x)*(1 + 3*x^2 + x^3). - Nikolaos Pantelidis, Feb 13 2023
Extensions
Offset changed from 1 to 0 by Harry J. Smith, Jul 25 2009
Comments