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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 (list; graph; refs; listen; history; text; internal format)
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.

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

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Last modified May 28 04:00 EDT 2020. Contains 334671 sequences. (Running on oeis4.)