A265188 Nonnegative m for which 3*floor(m^2/11) = floor(3*m^2/11).

0, 1, 5, 6, 10, 11, 12, 16, 17, 21, 22, 23, 27, 28, 32, 33, 34, 38, 39, 43, 44, 45, 49, 50, 54, 55, 56, 60, 61, 65, 66, 67, 71, 72, 76, 77, 78, 82, 83, 87, 88, 89, 93, 94, 98, 99, 100, 104, 105, 109, 110, 111, 115, 116, 120, 121, 122, 126, 127, 131, 132, 133, 137, 138, 142

Offset: 1

Author

Bruno Berselli, Dec 04 2015

Keywords

• nonn
• easy

Comments

See the second comment in A265187.

Also, nonnegative m congruent to 0, 1, 5, 6 or 10 (mod 11).

Primes in sequence: 5, 11, 17, 23, 43, 61, 67, 71, 83, 89, 109, 127, ...

Links

• Bruno Berselli, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

Crossrefs

Cf. A265187.

Cf. similar sequences provided by 3*floor(n^2/h) = floor(3*n^2/h): A005843 (h=2), A008585 (h=3), A001477 (h=4), A008854 (h=5), A047266 (h=6), A047299 (h=7), A042965 (h=8), A265227 (h=9), A054967 (h=10), this sequence (h=11), A047266 (h=12).

Programs

Magma

[n: n in [0..150] | 3*Floor(n^2/11) eq Floor(3*n^2/11)];

Mathematica

Select[Range[0, 150], 3 Floor[#^2/11] == Floor[3 #^2/11] &]
Select[Range[0, 150], MemberQ[{0, 1, 5, 6, 10}, Mod[#, 11]] &]
LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 1, 5, 6, 10, 11}, 70]

PARI

is(n) = 3*(n^2\11) == (3*n^2)\11 \\ Anders Hellström, Dec 05 2015

PARI

concat(0, Vec(x^2*(1 + 4*x + x^2 + 4*x^3 + x^4)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4)) + O(x^100))) \\ Michel Marcus, Dec 05 2015

Sage

[n for n in (0..150) if 3*floor(n^2/11) == floor(3*n^2/11)]

Formula

G.f.: x^2*(1 + 4*x + x^2 + 4*x^3 + x^4)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4)).

a(n) = a(n-1) + a(n-5) - a(n-6), n>6.