A264571 Number of (3+1)X(n+1) arrays of permutations of 0..n*4+3 with each element having directed index change 1,0 1,1 0,-1 or -1,1.

1, 4, 10, 44, 143, 633, 2172, 8409, 32046, 123607, 467535, 1782748, 6811612, 25977296, 98955733, 377295524, 1439130735, 5486977972, 20918581591, 79761954903, 304138808396, 1159628108611, 4421450347014, 16858598826709

Offset

1,2

Comments

Row 3 of A264569.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +41*a(n-4) -104*a(n-5) +14*a(n-6) +167*a(n-7) -715*a(n-8) +1169*a(n-9) -1018*a(n-10) -3680*a(n-11) +8691*a(n-12) -10335*a(n-13) +2525*a(n-14) +35277*a(n-15) -50582*a(n-16) +64373*a(n-17) +11060*a(n-18) -207508*a(n-19) +200293*a(n-20) -204582*a(n-21) -124748*a(n-22) +704108*a(n-23) -499827*a(n-24) +365700*a(n-25) +473743*a(n-26) -1541579*a(n-27) +729138*a(n-28) -331526*a(n-29) -929717*a(n-30) +2313138*a(n-31) -591289*a(n-32) +10149*a(n-33) +1058138*a(n-34) -2448606*a(n-35) +225766*a(n-36) +341725*a(n-37) -740229*a(n-38) +1867654*a(n-39) -9921*a(n-40) -441602*a(n-41) +343946*a(n-42) -1047499*a(n-43) -9489*a(n-44) +322880*a(n-45) -125643*a(n-46) +431100*a(n-47) -8968*a(n-48) -160742*a(n-49) +44437*a(n-50) -124400*a(n-51) +6980*a(n-52) +54449*a(n-53) -13758*a(n-54) +23185*a(n-55) -1859*a(n-56) -11695*a(n-57) +2887*a(n-58) -2532*a(n-59) +298*a(n-60) +1457*a(n-61) -383*a(n-62) +155*a(n-63) -26*a(n-64) -100*a(n-65) +29*a(n-66) -4*a(n-67) +a(n-68) +3*a(n-69) -a(n-70)

Example

Some solutions for n=4
..1..5..3..7..8....1..2..6..4..8....1..2..6..4..8....1..5..3..4..8
..0.10..2..9..4....0.10.11.12..3....0..7.11..9..3....6..0..2..9.13
.11.15..6.14.18....5.15..7.14..9....5.15.13.17.18...11.15.16..7.18
.16.17.12.19.13...16.17.18.19.13...16.10.12.19.14...10.17.12.19.14

Crossrefs

Cf. A264569.

Sequence in context: A149220 A149221 A149222 * A149223 A149224 A149225

Adjacent sequences: A264568 A264569 A264570 * A264572 A264573 A264574

Keyword

nonn

Author

R. H. Hardin, Nov 17 2015

Status

approved