OFFSET
1,2
COMMENTS
A001844(N) = N^2 + (N+1)^2 is divisible by 5 if and only if N=a(n), n>=1. E.g., n=2: 5|(3^2 + 4^2). But 7^2 + 8^2 is not congruent to 0 (mod 5). - Wolfdieter Lang, May 09 2012
The number of partitions of 5*(n-1) into at most 2 parts. - Colin Barker, Mar 31 2015
LINKS
David Lovler, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
a(n) = floor((5*n-3)/2). - Santi Spadaro, Jul 24 2001, corrected by Gary Detlefs, Oct 28 2011
G.f.: x*(1 + 2*x + 2*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Oct 07 2011
a(n) = 2*n + floor((n-1)/2) - 1. - Arkadiusz Wesolowski, Sep 19 2012
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(1/2 + sqrt(5)/10)*Pi/5 + log(phi)/sqrt(5), where phi is the golden ratio (A001622). - Amiram Eldar, Dec 07 2021
E.g.f.: 2 + ((10*x - 7)*exp(x) - exp(-x))/4. - David Lovler, Aug 23 2022
a(n) = a(n-1) + a(n-2) - a(n-3) for n >= 4. - Rémi Guillaume, Nov 22 2024
MATHEMATICA
Flatten[#+{1, 3}&/@(5*Range[0, 30])] (* Harvey P. Dale, Dec 22 2013 *)
PROG
(PARI) a(n)=(5*n-3)\2 \\ Charles R Greathouse IV, Oct 28 2011
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
STATUS
approved