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A250439 Number of (n+1)X(4+1) 0..2 arrays with nondecreasing sum of every two consecutive values in every row and column 1

%I

%S 3600,60000,1000000,8750000,76562500,450187500,2647102500,11859019200,

%T 53128406016,195165573120,716934758400,2263282560000,7144929000000,

%U 20012416875000,56053297265625,142499937937500,362266508890000

%N Number of (n+1)X(4+1) 0..2 arrays with nondecreasing sum of every two consecutive values in every row and column

%C Column 4 of A250443

%H R. H. Hardin, <a href="/A250439/b250439.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +18*a(n-2) -38*a(n-3) -152*a(n-4) +342*a(n-5) +798*a(n-6) -1938*a(n-7) -2907*a(n-8) +7752*a(n-9) +7752*a(n-10) -23256*a(n-11) -15504*a(n-12) +54264*a(n-13) +23256*a(n-14) -100776*a(n-15) -25194*a(n-16) +151164*a(n-17) +16796*a(n-18) -184756*a(n-19) +184756*a(n-21) -16796*a(n-22) -151164*a(n-23) +25194*a(n-24) +100776*a(n-25) -23256*a(n-26) -54264*a(n-27) +15504*a(n-28) +23256*a(n-29) -7752*a(n-30) -7752*a(n-31) +2907*a(n-32) +1938*a(n-33) -798*a(n-34) -342*a(n-35) +152*a(n-36) +38*a(n-37) -18*a(n-38) -2*a(n-39) +a(n-40)

%F Empirical for n mod 2 = 0: a(n) = (1/3131031158784)*n^20 + (7/195689447424)*n^19 + (493/260919263232)*n^18 + (2041/32614907904)*n^17 + (5281/3623878656)*n^16 + (34463/1358954496)*n^15 + (8369123/24461180928)*n^14 + (175039/47775744)*n^13 + (14323615/452984832)*n^12 + (28292321/127401984)*n^11 + (433413979/339738624)*n^10 + (254953261/42467328)*n^9 + (4413740701/191102976)*n^8 + (862554061/11943936)*n^7 + (723265463/3981312)*n^6 + (20008087/55296)*n^5 + (15399517/27648)*n^4 + (183817/288)*n^3 + (4095/8)*n^2 + 256*n + 60

%F Empirical for n mod 2 = 1: a(n) = (1/3131031158784)*n^20 + (7/195689447424)*n^19 + (2963/1565515579392)*n^18 + (4103/65229815808)*n^17 + (170759/115964116992)*n^16 + (420893/16307453952)*n^15 + (137540489/391378894848)*n^14 + (186200281/48922361856)*n^13 + (52127114249/1565515579392)*n^12 + (2583189377/10871635968)*n^11 + (120935995553/86973087744)*n^10 + (218008401281/32614907904)*n^9 + (41245572338777/1565515579392)*n^8 + (4142442582715/48922361856)*n^7 + (85987767005225/391378894848)*n^6 + (7389222103375/16307453952)*n^5 + (84109893284375/115964116992)*n^4 + (6293620178125/7247757312)*n^3 + (14136300171875/19327352832)*n^2 + (103730703125/268435456)*n + (413609765625/4294967296)

%e Some solutions for n=2

%e ..1..1..1..2..1....0..1..1..2..1....0..1..0..1..1....0..0..1..2..1

%e ..0..1..1..1..1....0..0..2..2..2....1..0..1..1..2....0..0..0..1..1

%e ..1..2..1..2..1....2..1..2..2..2....1..1..1..1..1....1..2..1..2..2

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 22 2014

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Last modified April 6 03:15 EDT 2020. Contains 333267 sequences. (Running on oeis4.)