A306469 Numbers not of the form x^2+2*y^2+2*y*z+4*z^2 (with x, y, z all >= 0).

7, 10, 14, 15, 21, 30, 35, 39, 42, 63, 70, 79, 84, 91, 94, 119, 126, 130, 133, 140, 168, 175, 182, 189, 210, 217, 231, 238, 259, 266, 280, 287, 315, 329, 336, 343, 359, 364, 378, 382, 385, 391, 399, 413, 427, 434, 462, 476, 483, 490, 511, 525, 532, 546, 560

Offset

1,1

Comments

It appears that the only terms not divisible by 7 are 10, 15, 30, 39, 79, 94, 130, 359, 382, 391, 754, and 1546. - Robert Israel, Mar 27 2019

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Irving Kaplansky, The first nontrivial genus of positive definite ternary forms, Mathematics of Computation, Vol. 64 (1995): 341-345.

Maple

N:= 1000: # for terms <= N
V:= Array(0..N):
for x from 0 while x^2<=N do
  for y from 0 while x^2 + 2*y^2 <= N do
    for z from 0 do
      v:= x^2 + 2*y^2 + 2*y*z + 4*z^2;
      if v > N then break fi;
      V[v]:= 1;
od od od:
select(t -> V[t]=0, [$1..N]); # Robert Israel, Mar 27 2019

Crossrefs

Cf. A097634 (without the nonnegative requirement).

Sequence in context: A123834 A064629 A215579 * A059752 A080205 A108980

Adjacent sequences: A306466 A306467 A306468 * A306470 A306471 A306472

Keyword

nonn

Author

N. J. A. Sloane, Mar 26 2019

Extensions

Thanks to Robert Israel for pointing out that I neglected to mention x, y, z >= 0. - N. J. A. Sloane, Mar 27 2019

Status

approved