login
A253195
Numbers congruent to 5 or 8 mod 9.
1
5, 8, 14, 17, 23, 26, 32, 35, 41, 44, 50, 53, 59, 62, 68, 71, 77, 80, 86, 89, 95, 98, 104, 107, 113, 116, 122, 125, 131, 134, 140, 143, 149, 152, 158, 161, 167, 170, 176, 179, 185, 188, 194, 197, 203, 206, 212, 215, 221, 224, 230, 233, 239, 242, 248, 251
OFFSET
1,1
COMMENTS
These numbers cannot be written as the sum of two triangular numbers.
FORMULA
a(n) = a(n-1) + a(n-2) - a(n-3), n >= 4.
G.f.: x*(5 + 3*x + x^2)/((1 + x)*(1 - x)^2).
a(n) = a(n-2) + 9.
a(n) = 9*n - a(n-1) - 5.
a(n) = 4*n + 2*ceiling(n/2) - floor(n/2) - 1.
a(n) = (9*n - (3/2)*(1 + (- 1)^n) + 1)/2.
E.g.f.: 1 + ((18*x - 1)*exp(x) - 3*exp(-x))/4. - David Lovler, Sep 06 2022
MATHEMATICA
LinearRecurrence[{1, 1, -1}, {5, 8, 14}, 56]
Select[Range[300], MemberQ[{5, 8}, Mod[#, 9]]&] (* Harvey P. Dale, Mar 17 2020 *)
PROG
(Magma) [n: n in [0..251] | n mod 9 in {5, 8}];
(PARI) Vec(x*(5 + 3*x + x^2)/((1 + x)*(1 - x)^2) + O(x^80)) \\ Michel Marcus, Mar 25 2015
CROSSREFS
Subsequence of A014132 and of A020757.
Sequence in context: A314476 A314477 A314478 * A314479 A314480 A314481
KEYWORD
nonn,easy
AUTHOR
STATUS
approved