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 A267654 Irregular triangle of palindromic subsequences. Every row has 2*n+1 terms. From the second row, there are only two alternated numbers: 2*n+4 and 2*n+2. 1
 2, 4, 2, 4, 6, 4, 6, 4, 6, 8, 6, 8, 6, 8, 6, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 16, 14, 16, 14, 16, 14, 16, 14, 16, 14, 16, 14, 16, 14, 16 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Row sums = 2, 10, 26, 50, ... = A069894(n). Starting from A053186(n) = 0,                            for b(n) 0, 1, 2,                              for c(n) 0, 1, 2, 3, 4,                                for d(n) 0, 1, 2, 3, 4, 5, 6, etc, a(n) is used for 1) b(n+1) = b(n) + (a(0)=2) i.e. 0, 2, 4, 6, ... = A005843(n). 2) c(n+3) = c(n) + (period 3:repeat 4, 2, 4) i.e. 0, 1, 2, 4, 3, 6, 8, ... =  A265667(n). 3) d(n+5) = d(n) + (period 5:repeat 6, 4, 6, 4, 6) i.e. 0, 1, 2, 3, 4, 6, 5, 8, 7, 10, ... = A265734(n). Etc. a(n) has a companion with the same terms,differently distributed,yielding permutations of the nonnegative numbers. See A265672. a(n) other writing (by pairs): 2,   4,  2,  4, 6,   4,  6,  4, 6,   8,  6,  8,  6,  8,  6,  8, 10   8, 10,  8, 10,  8, 10,  8, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, etc. First column: A168276(n+2). Second column: A168273(n+2). Row sums: 12, 20, 56, 72, ... = 4*A074378(n+1). The last term of the successive rows is the number of their terms. Main diagonal: A005843(n+1). LINKS FORMULA a(n) = 2 * A086520(n+2). a(2n) = 4*n + 2 times 4*n + 2 = 2, 2, 6, 6, 6, 6, 6, 6, 10,.... a(2n+1) = 4*(n+1) times 4*(n+1) = 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 12, .... EXAMPLE The triangle is 2, 4, 2, 4, 6, 4, 6, 4, 6, 8, 6, 8, 6, 8, 6, 8, etc. MATHEMATICA Table[2 (n - 1) + 2 (Boole@ OddQ@ k + 1), {n, 0, 7}, {k, 2 n + 1}] // Flatten (* Michael De Vlieger, Jan 19 2016 *) CROSSREFS Cf. A007395, A005843, A008586, A016825, A053186, A069894, A074378, A086520, A168273, A168276, A265667, A265672, A265734. Sequence in context: A214850 A236186 A143271 * A128859 A047975 A112791 Adjacent sequences:  A267651 A267652 A267653 * A267655 A267656 A267657 KEYWORD nonn,tabf AUTHOR Paul Curtz, Jan 19 2016 STATUS approved

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Last modified February 28 11:08 EST 2020. Contains 332323 sequences. (Running on oeis4.)