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Numbers that are either +-2 (mod 5) or +-11 (mod 55).
5

%I #15 Mar 20 2023 10:38:57

%S 2,3,7,8,11,12,13,17,18,22,23,27,28,32,33,37,38,42,43,44,47,48,52,53,

%T 57,58,62,63,66,67,68,72,73,77,78,82,83,87,88,92,93,97,98,99,102,103,

%U 107,108,112,113,117,118,121,122,123,127,128,132,133,137,138

%N Numbers that are either +-2 (mod 5) or +-11 (mod 55).

%H G. E. Andrews, <a href="https://doi.org/10.1080/00029890.1987.12000659">Further Problems on Partitions</a>, The American Mathematical Monthly, Vol. 94, No. 5 (1987), 437-439.

%H <a href="/index/Rec#order_25">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

%F From _Colin Barker_, Dec 01 2019: (Start)

%F G.f.: x*(2 + x + 4*x^2 + x^3 + 3*x^4 + x^5 + x^6 + 4*x^7 + x^8 + 4*x^9 + x^10 + 4*x^11 + x^12 + 4*x^13 + x^14 + 4*x^15 + x^16 + 4*x^17 + x^18 + x^19 + 3*x^20 + x^21 + 4*x^22 + x^23 + 2*x^24) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)*(1 - x^2 + x^4)*(1 + x^4)*(1 - x^4 + x^8)).

%F a(n) = a(n-1) + a(n-24) - a(n-25) for n>25.

%F (End)

%Y Cf. A329779-A329784.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Nov 29 2019