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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
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
Sequence in context: A208904 A344479 A209754 * A256504 A205713 A254344
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.)