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A204542
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Numbers that are congruent to {1, 4, 11, 14} mod 15.
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3
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1, 4, 11, 14, 16, 19, 26, 29, 31, 34, 41, 44, 46, 49, 56, 59, 61, 64, 71, 74, 76, 79, 86, 89, 91, 94, 101, 104, 106, 109, 116, 119, 121, 124, 131, 134, 136, 139, 146, 149, 151, 154, 161, 164, 166, 169, 176, 179, 181, 184, 191, 194, 196, 199, 206, 209, 211, 214, 221, 224
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OFFSET
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1,2
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COMMENTS
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The exponents in the q-series for A204220 are the squares of the numbers of this sequence.
The product of any two terms belongs to the sequence and therefore also a(n)^2, a(n)^3, a(n)^4, etc. - Bruno Berselli, Nov 28 2012
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LINKS
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FORMULA
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G.f.: x * (1 + 3*x + 7*x^2 + 3*x^3 + x^4) / ((1-x) * (1-x^4)).
a(n) = -a(1-n), a(n) = 15 + a(n-4), a(n) = floor(15 * n / 4) - ((n + 1) mod 4) for all n in Z.
a(n) = (30*n+10*i^(n*(n+1))-3*(-1)^n+1)/8 -2, where i=sqrt(-1). - Bruno Berselli, Nov 28 2012
E.g.f.: (4 - 5*(sin(x) - cos(x)) + 3*(5*x - 2)*sinh(x) + 3*(5*x - 3)*cosh(x))/4. - Ilya Gutkovskiy, Jun 07 2016
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(2*(sqrt(5)+5))*Pi/15. - Amiram Eldar, Dec 30 2021
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EXAMPLE
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G.f. = x + 4*x^2 + 11*x^3 + 14*x^4 + 16*x^5 + 19*x^6 + 26*x^7 + 29*x^8 + 31*x^9 + ...
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MAPLE
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MATHEMATICA
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Select[Range[250], MemberQ[{1, 4, 11, 14}, Mod[#, 15]]&] (* or *) LinearRecurrence[{1, 0, 0, 1, -1}, {1, 4, 11, 14, 16}, 60] (* Harvey P. Dale, Apr 15 2015 *)
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PROG
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(PARI) {a(n) = (n * 15) \ 4 - (n + 1) % 4};
(PARI) {a(n) = if( n<1, -a(1-n), polcoeff( x * (1 + 3*x + 7*x^2 + 3*x^3 + x^4) / ((1-x) * (1-x^4)) + x * O(x^n), n))};
(Magma) [n : n in [0..100] | n mod 15 in [1, 4, 11, 14]]; // Wesley Ivan Hurt, Jun 07 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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