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 A140950 a(n) = A140944(n+1) - 3*A140944(n). 1
 1, -3, -1, 5, -6, 3, -11, 10, -12, -5, 21, -22, 20, -24, 11, -43, 42, -44, 40, -48, -21, 85, -86, 84, -88, 80, -96, 43, -171, 170, -172, 168, -176, 160, -192, -85, 341, -342, 340, -344, 336, -352, 320, -384, 171, -683, 682, -684, 680, -688 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Jacobsthal numbers appear twice: 1) A001045(n+2) signed, terms 0, 1, 3, 6, 10 (A000217); 2) A001045(n+1) signed, terms 0, 2, 5, 9 (n*(n+3)/2=A000096); between them are -3; 5, -6; -11, 10, -12; which appear (opposite sign) by rows in A140503 (1, -1, 2, 3, -2, 4) square. Consider the permutation of the nonnegative numbers 0, 2, 5, 9, 14, 20, 27, 1, 3, 6, 10, 15, 21, 28, 4, 7, 11, 16, 22, 29, 8, 12, 17, 23, 30, 13, 18, 24, 31, 19, 25, 32, 26, 33, 34, etc. The corresponding distribution of a(n) is 1, -1, 3, -5, 11, -21, 43, -3, 5, -11, 21, -43, 85, -171, -6, 10, -22, 42, -86, 170, -12, 20, -44, 84, -172, -24, 40, -88, 168, -48, 80, -176, -96, 160, -192, etc. Column sums: -2, -2, -10, -10, -42, -42, -170, ... duplicate of a bisection of -A078008(n+2). b(n)= 1, -1, 3, -5, 11, 21, ... = (-1)^n*A001045(n+1) = A077925(n). Every row is b(n) or b(n+2) multiplied by 1, -1, -2, -4, -8, -16, ..., essentially -A011782(n). LINKS Table of n, a(n) for n=0..49. MATHEMATICA T[0, 0] = 0; T[1, 0] = T[0, 1] = 1; T[0, n_] := T[0, n] = T[0, n - 1] + 2*T[0, n - 2]; T[d_, d_] = 0; T[d_, n_] := T[d, n] = T[d - 1, n + 1] - T[d - 1, n]; A140944 = Table[T[d, n], {d, 0, 10}, {n, 0, d}] // Flatten; a[n_] := A140944[[n + 2]] - 3*A140944[[n + 1]]; Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Dec 18 2014 *) CROSSREFS Cf. A000096, A000217, A005015, A001045, A007283, A020988, A077925, A078008, A140503, A146523, A151575, A175805, A084247. Sequence in context: A208904 A344479 A209754 * A256504 A205713 A254344 Adjacent sequences: A140947 A140948 A140949 * A140951 A140952 A140953 KEYWORD sign,tabl AUTHOR Paul Curtz, Jul 25 2008 EXTENSIONS More terms and a(19)=-48 instead of 42 corrected by Jean-François Alcover, Dec 22 2014 STATUS approved

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Last modified May 24 18:59 EDT 2024. Contains 372781 sequences. (Running on oeis4.)