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A047452
Numbers that are congruent to {1, 6} mod 8.
19
1, 6, 9, 14, 17, 22, 25, 30, 33, 38, 41, 46, 49, 54, 57, 62, 65, 70, 73, 78, 81, 86, 89, 94, 97, 102, 105, 110, 113, 118, 121, 126, 129, 134, 137, 142, 145, 150, 153, 158, 161, 166, 169, 174, 177, 182, 185, 190
OFFSET
1,2
COMMENTS
Except for 1, numbers whose binary reflected Gray code (A014550) ends with 01. - Amiram Eldar, May 17 2021
FORMULA
G.f.: x*(1+5*x+2*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Dec 07 2011
E.g.f.: (4 + exp(-x) + (8*x - 5)*exp(x))/2. - Ilya Gutkovskiy, May 25 2016
a(n) = A047615(n) + 1. - Franck Maminirina Ramaharo, Jul 23 2018
Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2)+2)*Pi/16 + log(2)/8 + sqrt(2)*log(sqrt(2)+1)/8. - Amiram Eldar, Dec 11 2021
MAPLE
seq(coeff(series(factorial(n)*((4+exp(-x)+(8*x-5)*exp(x))/2), x, n+1), x, n), n=1..60); # Muniru A Asiru, Jul 24 2018
MATHEMATICA
Table[(8 n - 5 + (-1)^n)/2, {n, 1, 100}] (* Franck Maminirina Ramaharo, Jul 23 2018 *)
CoefficientList[ Series[(2x^2 + 5x + 1)/((x - 1)^2 (x + 1)), {x, 0, 50}], x] (* or *)
LinearRecurrence[{1, 1, -1}, {1, 6, 9}, 51] (* Robert G. Wilson v, Jul 24 2018 *)
PROG
(Maxima) makelist((8*n - 5 + (-1)^n)/2, n, 1, 100); /* Franck Maminirina Ramaharo, Jul 23 2018 */
(GAP) Filtered([0..250], n->n mod 8=1 or n mod 8=6); # Muniru A Asiru, Jul 24 2018
(Python)
def A047452(n): return (n<<2)-2-(n&1) # Chai Wah Wu, Mar 30 2024
KEYWORD
nonn,easy
STATUS
approved