0,6

Alois P. Heinz, Table of n, a(n) for n = 0..3699

Wikipedia, Pentomino

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 3, 8, 8, 12, 4, 2, 11, 10, 5, -1, -29, -90, -65, -20, 39, -13, -73, -71, -110, -128, -67, 44, 82, 0, -53, 67, 70, 61, -79, -96, -3, 79, 84, 64, 30, -42, -29, -44, 24, 0, 0, 2).

G.f.: (16*x^42 -16*x^41 +3*x^40 -20*x^39 -28*x^38 +28*x^37 -2*x^36 +31*x^35 +15*x^34 -38*x^33 -29*x^32 +9*x^31 +20*x^30 +69*x^29 +3*x^28 -10*x^27 +10*x^26 +2*x^25 +31*x^24 -10*x^23 -20*x^22 -41*x^21 -37*x^20 -25*x^19 +7*x^18 +8*x^17 -3*x^16 -28*x^15 -31*x^14 -9*x^13 +x^12 +2*x^11 +7*x^10 +6*x^9 -2*x^8 +4*x^7 +2*x^6 +4*x^5 +3*x^4 -1) / (2*x^45 +24*x^42 -44*x^41 -29*x^40 -42*x^39 +30*x^38 +64*x^37 +84*x^36 +79*x^35 -3*x^34 -96*x^33 -79*x^32 +61*x^31 +70*x^30 +67*x^29 -53*x^28 +82*x^26 +44*x^25 -67*x^24 -128*x^23 -110*x^22 -71*x^21 -73*x^20 -13*x^19 +39*x^18 -20*x^17 -65*x^16 -90*x^15 -29*x^14 -x^13 +5*x^12 +10*x^11 +11*x^10 +2*x^9 +4*x^8 +12*x^7 +8*x^6 +8*x^5 +3*x^4 -1).

a(7) = 8:

._____________. ._____________. ._____________.

|_. .___| | ._| |_. .___| ._| | | |_. .___| ._|

| |_| .___| | | | |_|_. | |_. | | ._|_| ._| | |

| ._|_| |___| | | |_. | |___| | | | ._| |___| |

| | .___| |_. | (4) | ._| |___| |_| (2) |_| |___| |_. | (2)

|_|_|_______|_| |_|___|_______| |___|_______|_| .

.

Cf. A174249, A343529, A349187.

Sequence in context: A244850 A188930 A332331 * A159576 A199626 A372790

Adjacent sequences: A352418 A352419 A352420 * A352422 A352423 A352424

nonn,easy

Alois P. Heinz, Apr 25 2022

approved