A253195 Numbers congruent to 5 or 8 mod 9.

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.

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

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

Adjacent sequences: A253192 A253193 A253194 * A253196 A253197 A253198

Keyword

nonn,easy

Author

Arkadiusz Wesolowski, Mar 24 2015

Status

approved