Original entry on oeis.org
3, 11, 37, 79, 137, 211, 821, 991, 1597, 1831, 2081, 2347, 2927, 3571, 3917, 4657, 5051, 6329, 8779, 9871, 11027, 14197, 14879, 17021, 20101, 21737, 26107, 27967, 28921, 33931, 34981, 39341, 40471, 41617, 50087, 51361, 59341, 60727, 62129, 66431, 69379, 70877
Offset: 1
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Select[Table[(1/2)*(1 + (-1)^n + 2*n + 4*n^2),{n,1,300}], PrimeQ]
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for(n=0, 300, if(ispseudoprime(t=(1/2)*(1 + (-1)^n + 2*n + 4*n^2)), print1(t", ")));
A304487
a(n) = (3 + 2*n - 3*n^2 + 4*n^3 - 3*((-1 + n) mod 2))/6.
Original entry on oeis.org
1, 4, 15, 36, 73, 128, 207, 312, 449, 620, 831, 1084, 1385, 1736, 2143, 2608, 3137, 3732, 4399, 5140, 5961, 6864, 7855, 8936, 10113, 11388, 12767, 14252, 15849, 17560, 19391, 21344, 23425, 25636, 27983, 30468, 33097, 35872, 38799, 41880, 45121, 48524, 52095
Offset: 1
For n = 1 the matrix A is
1
with trace Tr(A) = a(1) = 1.
For n = 2 the matrix A is
1, 2
4, 3
with Tr(A) = a(2) = 4.
For n = 3 the matrix A is
1, 2, 3
8, 9, 4
7, 6, 5
with Tr(A) = a(3) = 15.
For n = 4 the matrix A is
1, 2, 3, 4
12, 13, 14, 5
11, 16, 15, 6
10, 9, 8, 7
with Tr(A) = a(4) = 36.
Cf.
A126224 (determinant of the matrix A),
A317298 (first differences).
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a_n:=List([1..43], n->(3 + 2*n - 3*n^2 + 4*n^3 - 3*RemInt(-1 + n, 2))/6);
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List([1..43],n->(3+2*n-3*n^2+4*n^3-3*((-1+n) mod 2))/6); # Muniru A Asiru, Sep 17 2018
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I:=[1,4,15,36,73]; [n le 5 select I[n] else 3*Self(n-1)-2*Self(n-2)-2*Self(n-3)+3*Self(n-4)-Self(n-5): n in [1..43]]; // Vincenzo Librandi, Aug 26 2018
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seq((3+2*n-3*n^2+4*n^3-3*modp((-1+n),2))/6,n=1..43); # Muniru A Asiru, Sep 17 2018
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Table[1/6 (3 + 2 n - 3 n^2 + 4 n^3 - 3 Mod[-1 + n, 2]), {n, 1, 43}] (* or *)
CoefficientList[ Series[x*(1 + x + 5 x^2 + x^3)/((-1 + x)^4 (1 + x)), {x, 0, 43}], x] (* or *)
LinearRecurrence[{3, -2, -2, 3, -1}, {1, 4, 15, 36, 73}, 43]
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a(n):=(3 + 2*n - 3*n^2 + 4*n^3 - 3*mod(-1 + n, 2))/6$ makelist(a(n), n, 1, 43);
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Vec(x*(1 + x + 5*x^2 + x^3)/((-1 + x)^4*(1 + x)) + O(x^44))
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a(n) = (3 + 2*n - 3*n^2 + 4*n^3 - 3*((-1 + n)%2))/6
Showing 1-2 of 2 results.
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