A281550 Number of 2 X 2 matrices with all elements in 0..n such that the sum of the elements is prime.

0, 10, 46, 114, 234, 458, 826, 1370, 2090, 3010, 4174, 5658, 7534, 9930, 12954, 16662, 21074, 26242, 32246, 39182, 47186, 56386, 66874, 78798, 92290, 107434, 124282, 142942, 163550, 186266, 211250, 238626, 268526, 301134, 336610, 375086, 416678, 461454, 509434, 560662, 615182, 673106

Offset

0,2

Links

Charles R Greathouse IV, Table of n, a(n) for n = 0..10000 (terms 0..200 from Indranil Ghosh, terms 201..3000 from Chai Wah Wu)

Example

For n = 4, a few of the possible matrices are [0,4;2,1], [0,4;3,0], [0,4;3,4], [0,4;4,3], [1,0;0,1], [1,0;0,2], [1,0;0,4], [1,0;1,0], [1,0;1,1], [1,0;1,3], [2,2;3,0], [2,2;3,4], [2,2;4,3], [2,3;0,0], [2,3;0,2], [3,4;3,3], [3,4;4,0], [3,4;4,2], [4,0;0,1], [4,0;0,3], [4,0;1,0], ... There are 234 possibilities.
Here each of the matrices M is defined as M = [a,b;c,d] where a = M[1][1], b = M[1][2], c = M[2][1], d = M[2][2]. So, a(4) = 234.

Prog

(Python)
from sympy import isprime
def t(n):
....s=0
....for a in range(0, n+1):
........for b in range(0, n+1):
............for c in range(0, n+1):
................for d in range(0, n+1):
....................if isprime(a+b+c+d)==True:
........................s+=1
....return s
for i in range(0, 201):
....print str(i)+" "+str(t(i))
(PARI) a(n)=my(X=Pol(vector(n+1, i, 1))+O('x^(4*n)), Y=X^4, s); forprime(p=2, 4*n, s+=polcoeff(Y, p)); s \\ Charles R Greathouse IV, Feb 15 2017

Crossrefs

Cf. A210000, A281090, A281315.

Sequence in context: A007941 A007940 A082604 * A248575 A341404 A320697

Adjacent sequences: A281547 A281548 A281549 * A281551 A281552 A281553

Keyword

nonn

Author

Indranil Ghosh, Jan 23 2017

Status

approved