OFFSET
1,2
COMMENTS
Numbers such that the n-th triangular number is divisible by 4. - Charles R Greathouse IV, Apr 07 2011
Except for 0, numbers whose binary reflected Gray code (A014550) ends with 00. - Amiram Eldar, May 17 2021
LINKS
David Lovler, Table of n, a(n) for n = 1..10000
Lars Pos, Met kleine stapjes grote sprongen make, Pythagoras 61-4. Solutions of returning to the origin after steps of increasing width 1,2,3,.. in the 4 directions on a square grid (in Dutch).
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
a(n) = 8*n - a(n-1) - 9 (with a(1)=0). - Vincenzo Librandi, Aug 06 2010
From R. J. Mathar, Oct 08 2011: (Start)
a(n) = 3*(-1)^n/2 - 5/2 + 4*n.
G.f.: x^2*(7+x) / ( (1+x)*(x-1)^2 ). (End)
a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=7 and b(k)=2^(k+2) for k > 0. - Philippe Deléham, Oct 17 2011
Sum_{n>=2} (-1)^n/a(n) = log(2)/2 + sqrt(2)*log(sqrt(2)+1)/8 - (sqrt(2)+1)*Pi/16. - Amiram Eldar, Dec 18 2021
E.g.f.: 1 + ((8*x -5)*exp(x) + 3*exp(-x))/2. David Lovler, Aug 22 2022
MATHEMATICA
{#, #+7}&/@(8*Range[0, 30])//Flatten (* or *) LinearRecurrence[{1, 1, -1}, {0, 7, 8}, 60] (* Harvey P. Dale, Oct 30 2016 *)
PROG
(R)
kmax <- 10 # by choice
a <- c(0, 7)
for(k in 3:kmax) a <- c(a, a + 2^k)
a
# Yosu Yurramendi, Jan 18 2022
(PARI) a(n) = 4*n - 5/2 + 3*(-1)^n/2; \\ David Lovler, Jul 25 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Aug 06 2010
STATUS
approved