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 A228218 T(n,k)=Number of second differences of arrays of length n+2 of numbers in 0..k 13
 5, 9, 15, 13, 49, 31, 17, 103, 199, 63, 21, 177, 625, 665, 127, 25, 271, 1429, 3151, 2059, 255, 29, 385, 2731, 9705, 14053, 6305, 511, 33, 519, 4651, 23351, 58141, 58975, 19171, 1023, 37, 673, 7309, 47953, 176851, 320481, 242461, 58025, 2047, 41, 847, 10825 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts ....5......9......13.......17........21.........25.........29..........33 ...15.....49.....103......177.......271........385........519.........673 ...31....199.....625.....1429......2731.......4651.......7309.......10825 ...63....665....3151.....9705.....23351......47953......88215......149681 ..127...2059...14053....58141....176851.....439927.....951049.....1854553 ..255...6305...58975...320481...1225631....3693505....9399615....21108545 ..511..19171..242461..1688101...8006491...29066311...86929081...224817481 .1023..58025..989527..8717049..50556551..219071473..766106895..2276277137 .2047.175099.4017157.44633821.313882531.1609259287.6537612649.22222129177 LINKS R. H. Hardin, Table of n, a(n) for n = 1..310 FORMULA Empirical for column k: k=1: a(n) = 3*a(n-1) -2*a(n-2) for n>3 k=2: a(n) = 5*a(n-1) -6*a(n-2) for n>5 k=3: a(n) = 7*a(n-1) -12*a(n-2) for n>7 k=4: a(n) = 9*a(n-1) -20*a(n-2) for n>9 k=5: a(n) = 11*a(n-1) -30*a(n-2) for n>11 k=6: a(n) = 13*a(n-1) -42*a(n-2) for n>13 k=7: a(n) = 15*a(n-1) -56*a(n-2) for n>15 Empirical for row n: n=1: a(n) = 4*n + 1 n=2: a(n) = 10*n^2 + 4*n + 1 n=3: a(n) = 20*n^3 + 9*n^2 + 1*n + 1 n=4: a(n) = 35*n^4 + 14*n^3 - 17*n^2 + 30*n + 1 n=5: a(n) = 56*n^5 + 14*n^4 - 108*n^3 + 289*n^2 - 125*n + 1 n=6: a(n) = 84*n^6 - 402*n^4 + 1656*n^3 - 1860*n^2 + 776*n + 1 n=7: a(n) = 120*n^7 - 42*n^6 - 1158*n^5 + 6945*n^4 - 13980*n^3 + 13512*n^2 - 4887*n + 1 EXAMPLE Some solutions for n=4 k=4 ..4...-5....3...-3....6...-4...-3...-5...-8....1....5...-2....4...-3...-1...-6 .-6....7....1...-2...-6....1....4....5....6...-5...-5....1....0....0...-3....4 ..2...-3...-1....5....4....2....0...-2...-2....5....7....1....0...-3....3....1 .-2...-1...-2...-1...-6....0...-4....4....1....2...-7....1....4....6...-4...-6 CROSSREFS Row 1 is A004766 Sequence in context: A107980 A163161 A188358 * A314993 A314994 A106503 Adjacent sequences:  A228215 A228216 A228217 * A228219 A228220 A228221 KEYWORD nonn,tabl AUTHOR R. H. Hardin Aug 16 2013 STATUS approved

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Last modified September 22 16:41 EDT 2019. Contains 327311 sequences. (Running on oeis4.)