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A281550 Number of 2 X 2 matrices with all elements in 0..n such that the sum of the elements is prime. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A320697 A081583

Adjacent sequences:  A281547 A281548 A281549 * A281551 A281552 A281553

KEYWORD

nonn

AUTHOR

Indranil Ghosh, Jan 23 2017

STATUS

approved

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Last modified September 26 16:43 EDT 2020. Contains 337374 sequences. (Running on oeis4.)