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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. A228212 (k=2), A228213 (k=3), A228213 (k=4), A228215 (k=5). Sequence in context: A163161 A331556 A188358 * A361993 A314993 A314994 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 November 28 19:28 EST 2023. Contains 367419 sequences. (Running on oeis4.)