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A189146 Number of n X 3 array permutations with each element making zero or one knight moves. 1
1, 4, 49, 569, 4372, 42689, 412189, 3988132, 38271921, 375573977, 3665309372, 35872284105, 350949375581, 3439343559628, 33682318930233, 330021363385529, 3233215326749252, 31680809629578289, 310402921706993341 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column 3 of A189150.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..200

FORMULA

Empirical: a(n) = 9*a(n-1) +48*a(n-2) -371*a(n-3) +173*a(n-4) -4636*a(n-5) -21700*a(n-6) +321034*a(n-7) -261016*a(n-8) -939316*a(n-9) +8804712*a(n-10) -89239632*a(n-11) +89709648*a(n-12) +830637056*a(n-13) -2499914752*a(n-14) +6390654336*a(n-15) -987233536*a(n-16) -98495866880*a(n-17) +227291122176*a(n-18) -22499119616*a(n-19) -574642074624*a(n-20) +4090433287168*a(n-21) -8710999644160*a(n-22) -9262792159232*a(n-23) +33961426997248*a(n-24) -59705619185664*a(n-25) +164268932415488*a(n-26) +206996041138176*a(n-27) -959952477028352*a(n-28) +148261211865088*a(n-29) +225201818959872*a(n-30) -528765464084480*a(n-31) +2794884482203648*a(n-32) +3264721555816448*a(n-33) +9397359024799744*a(n-34) -32363504358916096*a(n-35) -14560459025809408*a(n-36) +41205664512475136*a(n-37) -65070379105779712*a(n-38) +117763114509795328*a(n-39) -26803976066301952*a(n-40) +132124530591137792*a(n-41) +236469835482005504*a(n-42) -1308758689225637888*a(n-43) +382298681149227008*a(n-44) +1688786500906385408*a(n-45) -1092767223451222016*a(n-46) -1774519408253730816*a(n-47) +3781671287689052160*a(n-48) -211699968811991040*a(n-49) -6414401302863806464*a(n-50) +3737846953229156352*a(n-51) +2510967898491584512*a(n-52) +740560663725735936*a(n-53) -4415779434636771328*a(n-54) +2508504992445366272*a(n-55) +54043195528445952*a(n-56) -1152921504606846976*a(n-57) +576460752303423488*a(n-58)

Contribution from Vaclav Kotesovec, Sep 01 2012: (Start)

Empirical: G.f.: -(1 - 8*x - 53*x^2 + 336*x^3 + 134*x^4 + 2846*x^5 + 19852*x^6 - 260036*x^7 + 6880*x^8 + 1292304*x^9 - 4702832*x^10 + 63471872*x^11 - 41560704*x^12 - 709453568*x^13 + 1351929600*x^14 - 3128104192*x^15 - 659457024*x^16 + 70691011072*x^17 - 106136367104*x^18 - 132922614784*x^19 + 318303350784*x^20 - 2065904152576*x^21 + 3225670889472*x^22 + 10372375166976*x^23 - 11884683280384*x^24 + 821650128896*x^25 - 70221817905152*x^26 - 122303538593792*x^27 + 415569654579200*x^28 + 388617697755136*x^29 - 457567875104768*x^30 + 122123978801152*x^31 - 134229549645824*x^32 - 7331344765943808*x^33 - 2581369716736000*x^34 + 28061409178812416*x^35 + 3074337254932480*x^36 - 27158215842070528*x^37 + 16916901758238720*x^38 - 8637373579526144*x^39 - 42490723492167680*x^40 - 200005314030862336*x^41 + 176918825432776704*x^42 + 705725146060554240*x^43 - 362309834634166272*x^44 - 1007318127542796288*x^45 + 222508717868843008*x^46 + 1439135376433217536*x^47 - 1225049467388952576*x^48 - 273971909362712576*x^49 + 2010997971109281792*x^50 - 2011772027295236096*x^51 + 145522562959409152*x^52 + 534802455750246400*x^53 + 22517998136852480*x^54 - 288230376151711744*x^55 + 144115188075855872*x^56)/( - 1 + 9*x + 48*x^2 - 371*x^3 + 173*x^4 - 4636*x^5 - 21700*x^6 + 321034*x^7 - 261016*x^8 - 939316*x^9 + 8804712*x^10 - 89239632*x^11 + 89709648*x^12 + 830637056*x^13 - 2499914752*x^14 + 6390654336*x^15 - 987233536*x^16 - 98495866880*x^17 + 227291122176*x^18 - 22499119616*x^19 - 574642074624*x^20 + 4090433287168*x^21 - 8710999644160*x^22 - 9262792159232*x^23 + 33961426997248*x^24 - 59705619185664*x^25 + 164268932415488*x^26 + 206996041138176*x^27 - 959952477028352*x^28 + 148261211865088*x^29 + 225201818959872*x^30 - 528765464084480*x^31 + 2794884482203648*x^32 + 3264721555816448*x^33 + 9397359024799744*x^34 - 32363504358916096*x^35 - 14560459025809408*x^36 + 41205664512475136*x^37 - 65070379105779712*x^38 + 117763114509795328*x^39 - 26803976066301952*x^40 + 132124530591137792*x^41 + 236469835482005504*x^42 - 1308758689225637888*x^43 + 382298681149227008*x^44 + 1688786500906385408*x^45 - 1092767223451222016*x^46 - 1774519408253730816*x^47 + 3781671287689052160*x^48 - 211699968811991040*x^49 - 6414401302863806464*x^50 + 3737846953229156352*x^51 + 2510967898491584512*x^52 + 740560663725735936*x^53 - 4415779434636771328*x^54 + 2508504992445366272*x^55 + 54043195528445952*x^56 - 1152921504606846976*x^57 + 576460752303423488*x^58)

Asymptotic: 0.045707910845127735589456 * 9.7983760587433722777622517835675^n

(End)

EXAMPLE

Some solutions for 4 X 3:

..0..8..3....0..1..2....0..1..7....0..8..7....5..1..2....0..1..7....7..6..3

..2..9..6....8.11.10....3..4..6....3..9.10....8..9..0....8..4..5....2..4.10

..5..7..1....6..7..3....5..2..9...11..2..1....6..7..3...11..2..3....1..0..9

..4.10.11....9..5..4....8.10.11....4..5..6....4.10.11....9.10..6....8..5.11

CROSSREFS

Sequence in context: A198971 A273230 A199028 * A086094 A055793 A202829

Adjacent sequences:  A189143 A189144 A189145 * A189147 A189148 A189149

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 17 2011

STATUS

approved

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Last modified February 21 20:22 EST 2020. Contains 332111 sequences. (Running on oeis4.)