

A061600


a(n) = n^3  n + 1.


6



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


COMMENTS

Smallest of n consecutive odd numbers whose sum is n^4. (n^k can be expressed as the sum of n consecutive odd numbers the smallest of which is given by n^(k1)n+1.)


REFERENCES

T. A. Gulliver, Sequences from Cubes of Integers, Int. Math. Journal, 4 (2003), 439445.


LINKS

Harry J. Smith, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,6,4,1).


FORMULA

G.f.: (13*x+9*x^2x^3)/(1  x)^4. a(n) = A126420(n).  Bruno Berselli, Aug 29 2011
a(n) = 1 + Sum_{k=1..n} 3*(k1)*k.  Luce ETIENNE and Michel Marcus, Nov 01 2014


EXAMPLE

a(5) = 121 = 5^3  5 + 1. We have 121 + 123 + 125 + 127 + 129 = 625 = 5^4.


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 *)


PROG

(PARI) { for (n=0, 1000, write("b061600.txt", n, " ", n^3  n + 1) ) } \\ Harry J. Smith, Jul 25 2009
(MAGMA) [n^3  n + 1: n in [0..40]]; // Vincenzo Librandi, Aug 29 2011


CROSSREFS

Sequence in context: A034135 A212136 A213392 * A098538 A033814 A321165
Adjacent sequences: A061597 A061598 A061599 * A061601 A061602 A061603


KEYWORD

nonn,easy


AUTHOR

Amarnath Murthy, May 19 2001


EXTENSIONS

Offset changed from 1 to 0 by Harry J. Smith, Jul 25 2009


STATUS

approved



