A306278 Numbers congruent to 2 or 11 mod 14.
2, 11, 16, 25, 30, 39, 44, 53, 58, 67, 72, 81, 86, 95, 100, 109, 114, 123, 128, 137, 142, 151, 156, 165, 170, 179, 184, 193, 198, 207, 212, 221, 226, 235, 240, 249, 254, 263, 268, 277, 282, 291, 296, 305, 310, 319, 324, 333, 338, 347, 352, 361, 366, 375, 380, 389, 394
Offset: 1
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
Crossrefs
Programs
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Maple
seq(seq(14*i+j, j=[2, 11]), i=0..28);
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Mathematica
Flatten[Table[{14n + 2, 14n + 11}, {n, 0, 28}]] LinearRecurrence[{1,1,-1},{2,11,16},60] (* Harvey P. Dale, Jan 16 2023 *) -
PARI
for(n=2, 394, if((n%14==2) || (n%14==11), print1(n, ", ")))
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PARI
for(n=1,57,print1(7*n-4+(-1)^n,", "))
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PARI
for(n=1,500,if(n%14==2,print1(n,", "));if(n%14==11,print1(n,", "))) \\ Jinyuan Wang, Feb 03 2019
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PARI
Vec(x*(2 + 9*x + 3*x^2) / ((1 - x)^2*(1 + x)) + O(x^40)) \\ Colin Barker, Mar 14 2019
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PARI
upto(n) = forstep(i = 2, n, [9, 5], print1(i", ")) \\ David A. Corneth, Mar 27 2019
Formula
a(n) = 7*n - A010703(n).
a(n) = 7*n - 4 + (-1)^n.
a(n) = a(n - 1) + a(n - 2) - a(n - 3) for n > 3.
From Jinyuan Wang, Feb 03 2019: (Start)
For odd number k, a(k) = 7*k - 5.
For even number k, a(k) = 7*k - 3.
(End)
G.f.: x*(2 + 9*x + 3*x^2) / ((1 - x)^2*(1 + x)). - Colin Barker, Mar 14 2019
E.g.f.: 3 + (7*x - 4)*exp(x) + exp(-x). - David Lovler, Sep 07 2022