A394276 Number of induced cubes in the n-triangular honeycomb queen graph.

1, 6, 21, 67, 168, 369, 733, 1350, 2328, 3823, 6009, 9114, 13399, 19185, 26811, 36742, 49371, 65328, 85141, 109401, 139242, 174397, 217977, 266778, 328954, 394065, 481209, 564856, 685329, 788829, 953575, 1076730, 1300005, 1440346, 1740597, 1892463, 2293372

Offset

1,2

Links

Table of n, a(n) for n=1..37.

Eric Weisstein's World of Mathematics, Cube Polynomial.

Eric Weisstein's World of Mathematics, Triangular Honeycomb Queen Graph.

Index entries for linear recurrences with constant coefficients, signature (0,7,0,-21,0,35,0,-35,0,21,0,-7,0,1).

Formula

a(n) = 7*a(n-2)-21*a(n-4)+35*a(n-6)-35*a(n-8)+21*a(n-10)-7*a(n-12)+a(n-14).

G.f.: x*(-1-6*x-14*x^2-25*x^3-42*x^4-26*x^5+37*x^6+36*x^7-25*x^8+13*x^9+60*x^10-7*x^11-15*x^12+30*x^13)/(-1+x^2)^7.

Mathematica

Table[Piecewise[{{(-460800 + 561408 n - 242720 n^2 + 57240 n^3 - 5060 n^4 + 762 n^5 - 5 n^6)/15360, Mod[n, 2] == 0}, {(6645 - 9071 n + 3550 n^2 + 70 n^3 + 45 n^4 + 41 n^5)/1280, Mod[n, 2] == 1}}], {n, 20}]
LinearRecurrence[{0, 7, 0, -21, 0, 35, 0, -35, 0, 21, 0, -7, 0, 1}, {1, 6, 21, 67, 168, 369, 733, 1350, 2328, 3823, 6009, 9114, 13399, 19185}, 20]
CoefficientList[Series[(-1 - 6 x - 14 x^2 - 25 x^3 - 42 x^4 - 26 x^5 + 37 x^6 + 36 x^7 - 25 x^8 + 13 x^9 + 60 x^10 - 7 x^11 - 15 x^12 + 30 x^13)/(-1 + x^2)^7, {x, 0, 20}], x]

Crossrefs

Sequence in context: A105457 A134931 A119103 * A180795 A306089 A107653

Adjacent sequences: A394273 A394274 A394275 * A394277 A394278 A394279

Keyword

nonn,easy

Author

Eric W. Weisstein, Mar 14 2026

Status

approved