The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A280344 Number of 2 X 2 matrices with all elements in {0,...,n} with determinant = permanent^n. 2
 0, 12, 30, 56, 90, 132, 182, 240, 306, 380, 462, 552, 650, 756, 870, 992, 1122, 1260, 1406, 1560, 1722, 1892, 2070, 2256, 2450, 2652, 2862, 3080, 3306, 3540, 3782, 4032, 4290, 4556, 4830, 5112, 5402, 5700, 6006, 6320, 6642, 6972, 7310, 7656, 8010, 8372, 8742, 9120, 9506, 9900, 10302 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For n>0, a(n) is the perimeter of a primitive Pythagorean triangle. - Torlach Rush, Jul 11 2019 LINKS Indranil Ghosh, Table of n, a(n) for n = 0..995 FORMULA a(0) = A002939(0) = 0; a(n) = A002939(n+1), for n>=1. a(n) = (((n-2)*a(n-1))/(n-4)) - (6*(3*(n-1)+1)/(n-4)) for n>=4. Conjectures from Colin Barker, Jan 01 2017: (Start) a(n) = 2 + 6*n + 4*n^2 for n>0. a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3. G.f.: 2*x*(6 - 3*x + x^2) / (1 - x)^3. (End) From Torlach Rush, Jul 11 2019: (Start) a(n) = (2*n+1)*(2*n+2), n>0. a(n) = 2*((n+1)^2 + ((n+1)*n)), n>0. (End) MATHEMATICA Table[Boole[n != 0] 2 # (2 # - 1) &[n + 1], {n, 0, 50}] (* or *) CoefficientList[Series[2 x (6 - 3 x + x^2)/(1 - x)^3, {x, 0, 50}], x] (* Michael De Vlieger, Jan 01 2017 *) PROG (Python) 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 (a*d-b*c)==(a*d+b*c)**n:                         s+=1     return s for i in range(0, 41):     print str(i)+" "+str(t(i)) CROSSREFS Same as both A002939 and A118239 without A002939(1) = 2. Cf. A016754, A280343. Sequence in context: A111396 A080385 A120090 * A286497 A086830 A084699 Adjacent sequences:  A280341 A280342 A280343 * A280345 A280346 A280347 KEYWORD nonn AUTHOR Indranil Ghosh, Jan 01 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 27 12:10 EDT 2021. Contains 346306 sequences. (Running on oeis4.)