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 A181262 T(n,k) = number of (n+2) X (k+2) binary matrices with every 3 X 3 block having exactly four 1's. 9
 126, 336, 336, 906, 746, 906, 2484, 1684, 1684, 2484, 7218, 3942, 3190, 3942, 7218, 21024, 10348, 6360, 6360, 10348, 21024, 61398, 27554, 14974, 10818, 14974, 27554, 61398, 182520, 74784, 36244, 22512, 22512, 36244, 74784, 182520, 542754, 212570, 91122, 48846, 41374, 48846, 91122, 212570, 542754 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts: 126 336 906 2484 7218 21024 61398 182520 542754 336 746 1684 3942 10348 27554 74784 212570 608476 906 1684 3190 6360 14974 36244 91122 247372 681262 2484 3942 6360 10818 22512 48846 112500 289830 764832 7218 10348 14974 22512 41374 79324 162882 387076 952462 21024 27554 36244 48846 79324 133850 242784 526226 1196428 61398 74784 91122 112500 162882 242784 386406 750312 1548594 182520 212570 247372 289830 387076 526226 750312 1297322 2384308 542754 608476 681262 764832 952462 1196428 1548594 2384308 3873790 1614492 1755630 1906656 2072106 2438184 2877078 3449484 4777806 6881880 LINKS R. H. Hardin, Table of n, a(n) for n=1..219 David Radcliffe, Counting binary matrices with every 3 X 3 block having exactly four ones FORMULA Empirical column 1: a(n) = 3*a(n-1) + 12*a(n-3) - 36*a(n-4) - 27*a(n-6) + 81*a(n-7). Empirical column 2: a(n) = 4*a(n-1) - 3*a(n-2) + 32*a(n-3) - 128*a(n-4) + 96*a(n-5) - 375*a(n-6) + 1500*a(n-7) - 1125*a(n-8) + 1980*a(n-9) - 7920*a(n-10) + 5940*a(n-11) - 4644*a(n-12) + 18576*a(n-13) - 13932*a(n-14) + 3888*a(n-15) - 15552*a(n-16) + 11664*a(n-17). Empirical columns 3 and 4: a(n) = 4*a(n-1) - 3*a(n-2) + 36*a(n-3) - 144*a(n-4) + 108*a(n-5) - 503*a(n-6) + 2012*a(n-7) - 1509*a(n-8) + 3480*a(n-9) - 13920*a(n-10) + 10440*a(n-11) - 12564*a(n-12) + 50256*a(n-13) - 37692*a(n-14) + 22464*a(n-15) - 89856*a(n-16) + 67392*a(n-17) - 15552*a(n-18) + 62208*a(n-19) - 46656*a(n-20). Empirical columns 5 and 6: a(n) = 6*a(n-1) - 11*a(n-2) + 42*a(n-3) - 216*a(n-4) + 396*a(n-5) - 719*a(n-6) + 3018*a(n-7) - 5533*a(n-8) + 6498*a(n-9) - 20880*a(n-10) + 38280*a(n-11) - 33444*a(n-12) + 75384*a(n-13) - 138204*a(n-14) + 97848*a(n-15) - 134784*a(n-16) + 247104*a(n-17) - 150336*a(n-18) + 93312*a(n-19) - 171072*a(n-20) + 93312*a(n-21). All columns (provably) satisfy a(n) = 6*a(n-1) - 11*a(n-2) + 60*a(n-3) - 324*a(n-4) + 594*a(n-5) - 1475*a(n-6) + 6906*a(n-7) - 12661*a(n-8) + 19440*a(n-9) - 75204*a(n-10) + 137874*a(n-11) - 150408*a(n-12) + 451224*a(n-13) - 827244*a(n-14) + 699840*a(n-15) - 1491696*a(n-16) + 2734776*a(n-17) - 1911600*a(n-18) + 2519424*a(n-19) - 4618944*a(n-20) + 2799360*a(n-21) - 1679616*a(n-22) + 3079296*a(n-23) - 1679616*a(n-24). The characteristic polynomial for this recurrence is (x - 1)*(x - 2)*(x - 3)*(x^3 - 2)*(x^3 - 3)*(x^3 - 4)*(x^3 - 6)*(x^3 - 9)*(x^3 - 12)*(x^3 - 18). - David Radcliffe, Jan 14 2023 EXAMPLE Some solutions for 3 X 3: 1 1 0 0 0 1 1 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 1 1 1 1 CROSSREFS Cf. A181256, A181257, A181258, A181259, A181260, A181261 for columns 1-6. Sequence in context: A356143 A254465 A063334 * A181255 A329807 A322542 Adjacent sequences: A181259 A181260 A181261 * A181263 A181264 A181265 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Oct 10 2010 STATUS approved

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Last modified September 8 14:54 EDT 2024. Contains 375753 sequences. (Running on oeis4.)