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A253748 Number of (n+1)X(7+1) 0..2 arrays with every 2X2 subblock ne-sw antidiagonal difference nondecreasing horizontally and nw+se diagonal sum nondecreasing vertically 1
315576, 298760, 2363797, 7348144, 33767784, 106040628, 333213583, 871426149, 2111246736, 4561812863, 9330585017, 17842432139, 32535281473, 56464375423, 94767234632, 153713251358, 242566893076, 372616947142, 560429992326 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 7 of A253749

LINKS

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

FORMULA

Empirical: a(n) = 6*a(n-1) -15*a(n-2) +20*a(n-3) -10*a(n-4) -24*a(n-5) +74*a(n-6) -100*a(n-7) +65*a(n-8) +30*a(n-9) -145*a(n-10) +200*a(n-11) -140*a(n-12) +140*a(n-14) -200*a(n-15) +145*a(n-16) -30*a(n-17) -65*a(n-18) +100*a(n-19) -74*a(n-20) +24*a(n-21) +10*a(n-22) -20*a(n-23) +15*a(n-24) -6*a(n-25) +a(n-26) for n>41

Empirical for n mod 4 = 0: a(n) = (31/67200)*n^10 + (7751/60480)*n^9 + (466561/40320)*n^8 + (7477567/20160)*n^7 - (6191923/28800)*n^6 + (19844983/5760)*n^5 - (16432778519/161280)*n^4 + (43453946273/120960)*n^3 + (15278661557/8400)*n^2 - (226744085/28)*n - 1302534 for n>15

Empirical for n mod 4 = 1: a(n) = (31/67200)*n^10 + (7751/60480)*n^9 + (466561/40320)*n^8 + (7477567/20160)*n^7 - (6191923/28800)*n^6 + (19844983/5760)*n^5 - (16379257499/161280)*n^4 + (22983106039/60480)*n^3 + (279237392087/134400)*n^2 - (26796876895/2688)*n + (1031330999/512) for n>15

Empirical for n mod 4 = 2: a(n) = (31/67200)*n^10 + (7751/60480)*n^9 + (466561/40320)*n^8 + (7477567/20160)*n^7 - (6191923/28800)*n^6 + (19844983/5760)*n^5 - (16443929519/161280)*n^4 + (42972543743/120960)*n^3 + (12531654707/8400)*n^2 - (3312534991/672)*n - (272889211/32) for n>15

Empirical for n mod 4 = 3: a(n) = (31/67200)*n^10 + (7751/60480)*n^9 + (466561/40320)*n^8 + (7477567/20160)*n^7 - (6191923/28800)*n^6 + (19844983/5760)*n^5 - (16406990099/161280)*n^4 + (11087479997/30240)*n^3 + (235087208387/134400)*n^2 - (17381962057/2688)*n - (3516359385/512) for n>15

EXAMPLE

Some solutions for n=1

..0..0..2..2..2..1..1..1....0..0..0..2..2..1..2..2....0..0..0..0..1..1..2..2

..0..2..2..1..0..0..0..2....0..0..2..2..0..1..1..1....1..1..1..0..0..1..1..1

CROSSREFS

Sequence in context: A250501 A234656 A205984 * A253755 A309238 A153749

Adjacent sequences:  A253745 A253746 A253747 * A253749 A253750 A253751

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 11 2015

STATUS

approved

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Last modified June 12 10:58 EDT 2021. Contains 344947 sequences. (Running on oeis4.)