A092220 -id:A092220 - cp's OEIS frontend

A131531 Period 6: repeat [0, 0, 1, 0, 0, -1].

0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0

Offset: 1

Paul Curtz, Aug 26 2007

Also: partial sums of A092220 shifted by two indices. - R. J. Mathar, Feb 08 2008
From Paul Curtz, Jun 05 2011: (Start)
The square array of this sequence in the top row and further rows defined as first differences of preceding rows starts (see A167613):
.   0,   0,   1,   0,   0,  -1, ...
.   0,   1,  -1,   0,  -1,   1, ...  = A092220,
.   1,  -2,   1,  -1,   2,  -1, ...  = A131556,
.  -3,   3,  -2,   3,  -3    2, ...
.   6,  -5,   5,  -6,   5,  -5, ...
. -11,  10, -11,  11, -10,  11, ...
.  21, -21,  22, -21,  21, -22, ...
. -42,  43, -43,  42, -43,  43, ...
The main diagonal in this array is A001045; the first superdiagonal is the negated elements of A001045, the second superdiagonal is A078008.
The left column of the array is basically the inverse binomial transform, (-1)^n * A024495(n), assuming offset 0.
The second column of the array is A131708 with alternating signs, and the third column is A024493 with alternating signs (both assuming offset 0). (End)

Index entries for linear recurrences with constant coefficients, signature (0,0,-1).

Cf. A001045, A024493, A024495, A078008, A092220, A131556, A131708, A167613.

&cat[[0, 0, 1, 0, 0, -1]^^20]; // Wesley Ivan Hurt, Jun 20 2016

A131531:=n->[0, 0, 1, 0, 0, -1][(n mod 6)+1]: seq(A131531(n), n=0..100); # Wesley Ivan Hurt, Jun 20 2016

PadRight[{}, 120, {0,0,1,0,0,-1}] (* Harvey P. Dale, Nov 11 2012 *)

a(n)=[0,0,1,0,0,-1][n%6+1] \\ Charles R Greathouse IV, Jun 01 2011

G.f.: x^3/(x+1)/(x^2-x+1). - R. J. Mathar, Nov 14 2007
a(n) = (-A057079(n+1) - (-1)^n)/3. - R. J. Mathar, Jun 13 2011
a(n) = -cos(Pi*(n-1)/3)/3 + sin(Pi*(n-1)/3)/sqrt(3) - (-1)^n/3. - R. J. Mathar, Oct 08 2011
a(n) = ( (-1)^n - (-1)^floor((n+2)/3) )/2. - Bruno Berselli, Jul 09 2013
a(n) + a(n-3) = 0 for n > 3. - Wesley Ivan Hurt, Jun 20 2016

Edited by N. J. A. Sloane, Sep 15 2007

A112465 Riordan array (1/(1+x), x/(1-x)).

Original entry on oeis.org

1, -1, 1, 1, 0, 1, -1, 1, 1, 1, 1, 0, 2, 2, 1, -1, 1, 2, 4, 3, 1, 1, 0, 3, 6, 7, 4, 1, -1, 1, 3, 9, 13, 11, 5, 1, 1, 0, 4, 12, 22, 24, 16, 6, 1, -1, 1, 4, 16, 34, 46, 40, 22, 7, 1, 1, 0, 5, 20, 50, 80, 86, 62, 29, 8, 1, -1, 1, 5, 25, 70, 130, 166, 148, 91, 37, 9, 1, 1, 0, 6, 30, 95, 200, 296, 314, 239, 128, 46, 10, 1

Offset: 0

Paul Barry, Sep 06 2005

Inverse is A112466. Note that C(n,k) = Sum_{j = 0..n-k} C(j+k-1, j).

			Triangle starts
   1;
  -1, 1;
   1, 0, 1;
  -1, 1, 1,  1;
   1, 0, 2,  2,  1;
  -1, 1, 2,  4,  3,  1;
   1, 0, 3,  6,  7,  4,  1;
  -1, 1, 3,  9, 13, 11,  5, 1;
   1, 0, 4, 12, 22, 24, 16, 6, 1;
Production matrix begins
  -1, 1;
   0, 1, 1;
   0, 0, 1, 1;
   0, 0, 0, 1, 1;
   0, 0, 0, 0, 1, 1;
   0, 0, 0, 0, 0, 1, 1;
   0, 0, 0, 0, 0, 0, 1, 1;
   0, 0, 0, 0, 0, 0, 0, 1, 1; - _Paul Barry_, Apr 08 2011

Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened
Roland Bacher, Chebyshev polynomials, quadratic surds and a variation of Pascal's triangle, arXiv:1509.09054 [math.CO], 2015.
E. Deutsch, L. Ferrari and S. Rinaldi, Production Matrices, Advances in Mathematics, 34 (2005) pp. 101-122.
Index entries for triangles and arrays related to Pascal's triangle

Cf. A059260, A108561, A112466, A112468.
Columns: A033999(n) (k=0), A000035(n) (k=1), A004526(n) (k=2), A002620(n-1) (k=3), A002623(n-4) (k=4), A001752(n-5) (k=5), A001753(n-6) (k=6), A001769(n-7) (k=7), A001779(n-8) (k=8), A001780(n-9) (k=9), A001781(n-10) (k=10), A001786(n-11) (k=11), A001808(n-12) (k=12).
Diagonals: A000012(n) (k=n), A023443(n) (k=n-1), A152947(n-1) (k=n-2), A283551(n-3) (k=n-3).
Main diagonal: A072547.
Sums: A078008 (row), A078024 (diagonal), A092220 (signed diagonal), A280560 (signed row).

a112465 n k = a112465_tabl !! n !! k
a112465_row n = a112465_tabl !! n
a112465_tabl = iterate f [1] where
   f xs'@(x:xs) = zipWith (+) ([-x] ++ xs ++ [0]) ([0] ++ xs')
-- Reinhard Zumkeller, Jan 03 2014

A112465:= func< n,k | (-1)^(n+k)*(&+[(-1)^j*Binomial(j+k-1,j): j in [0..n-k]]) >;
[A112465(n,k): k in [0..n], n in [0..13]]; // G. C. Greubel, Apr 18 2025

T[n_, k_]:= Sum[Binomial[j+k-1, j]*(-1)^(n-k-j), {j, 0, n-k}];
Table[T[n,k], {n,0,12}, {k,0,n}]//Flatten (* Jean-François Alcover, Jul 23 2018 *)

def A112465(n,k): return (-1)^(n+k)*sum((-1)^j*binomial(j+k-1,j) for j in range(n-k+1))
print(flatten([[A112465(n,k) for k in range(n+1)] for n in range(13)])) # G. C. Greubel, Apr 18 2025

Number triangle T(n, k) = Sum_{j=0..n-k} (-1)^(n-k-j)*C(j+k-1, j).
T(2*n, n) = A072547(n) (main diagonal). - Paul Barry, Apr 08 2011
From Reinhard Zumkeller, Jan 03 2014: (Start)
T(n, k) = T(n-1, k-1) + T(n-1, k), 0 < k < n, with T(n, 0) = (-1)^n and T(n, n) = 1.
T(n, k) = A108561(n, n-k). (End)
T(n, k) = T(n-1, k-1) + T(n-2, k) + T(n-2, k-1), T(0, 0) = 1, T(1, 0) = -1, T(1, 1) = 1, T(n, k) = 0 if k < 0 or if k > n. - Philippe Deléham, Jan 11 2014
exp(x) * e.g.f. for row n = e.g.f. for diagonal n. For example, for n = 3 we have exp(x)*(-1 + x + x^2/2! + x^3/3!) = -1 + 2*x^2/2! + 6*x^3/3! + 13*x^4/4! + .... The same property holds more generally for Riordan arrays of the form ( f(x), x/(1 - x) ). - Peter Bala, Dec 21 2014

A131666 First differences of (A113405 prefixed with a 0).

Original entry on oeis.org

0, 0, 1, 1, 2, 3, 7, 14, 29, 57, 114, 227, 455, 910, 1821, 3641, 7282, 14563, 29127, 58254, 116509, 233017, 466034, 932067, 1864135, 3728270, 7456541, 14913081, 29826162, 59652323, 119304647, 238609294, 477218589, 954437177, 1908874354

Offset: 0

Paul Curtz, Sep 14 2007

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,0,-1,2).

a:=[0,0,1,1];; for n in [5..35] do a[n]:=2*a[n-1]-a[n-3]+2*a[n-4]; od; a; # G. C. Greubel, Nov 21 2019

R:=PowerSeriesRing(Integers(), 35); [0,0] cat Coefficients(R!( x^2*(1-x)/((1+x)*(1-2*x)*(1-x+x^2)) )); // G. C. Greubel, Nov 21 2019

seq(coeff(series(x^2*(1-x)/((1+x)*(1-2*x)*(1-x+x^2)), x, n+1), x, n), n = 0..35); # G. C. Greubel, Nov 21 2019

Table[(2*(-1)^n +2^n -3*((-1)^Floor[(n+1)/3] +(-1)^Floor[(n+2)/3])/2)/9, {n, 0, 35}] (* G. C. Greubel, Nov 21 2019 *)

my(x='x+O('x^35)); concat([0,0], Vec(x^2*(1-x)/((1+x)*(1-2*x)*(1-x+x^2)))) \\ G. C. Greubel, Nov 21 2019

def A131666_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P(x^2*(1-x)/((1+x)*(1-2*x)*(1-x+x^2))).list()
A131666_list(35) # G. C. Greubel, Nov 21 2019

a(n+1) - 2*a(n) = 0, 1, -1, 0, -1, 1, ... is the hexaperiodic A092220 (corrected Sep 24 2007).
O.g.f.: x^2*(1-x)/((1+x)*(1-2*x)*(1-x+x^2)). - R. J. Mathar, Nov 23 2007
a(n) = Sum_{k=0..n-2} A001045(n-k+1)*binomial(k,n-k-2). - Paul Barry, Apr 22 2009
a(n) = (1/18)*( 2^(n+1) + 4*(-1)^n - 3*((-1)^floor((n+1)/3) + (-1)^floor((n+2)/3)) ). - G. C. Greubel, Nov 21 2019

A167613 Array T(n,k) read by antidiagonals: the k-th term of the n-th difference of A131531.

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 0, -1, -2, -3, 0, 0, 1, 3, 6, -1, -1, -1, -2, -5, -11, 0, 1, 2, 3, 5, 10, 21, 0, 0, -1, -3, -6, -11, -21, -42, 1, 1, 1, 2, 5, 11, 22, 43, 85, 0, -1, -2, -3, -5, -10, -21, -43, -86, -171, 0, 0, 1, 3, 6, 11, 21, 42, 85, 171, 342, -1, -1, -1, -2, -5, -11, -22, -43, -85, -170, -341, -683, 0, 1, 2, 3, 5, 10, 21, 43, 86, 171, 341, 682, 1365

Offset: 0

Paul Curtz, Nov 07 2009

The array contains A131708(0) in diagonal 0, then -A024495(0..1) in diagonal 1, then A024493(0..2) in diagonal 2, then -A131708(0..3), then A024495(0..4), then -A024493(0..5).

			The table starts in row n=0 with columns k >= 0 as:
0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0 A131531
0, 1, -1, 0, -1, 1, 0, 1, -1, 0, -1, 1, 0, 1, -1, 0, -1, 1, 0, 1, -1 A092220
1, -2, 1, -1, 2, -1, 1, -2, 1, -1, 2, -1, 1, -2, 1, -1, 2, -1, 1, -2 A131556
-3, 3, -2, 3, -3, 2, -3, 3, -2, 3, -3, 2, -3, 3, -2, 3, -3, 2, -3 A164359
6, -5, 5, -6, 5, -5, 6, -5, 5, -6, 5, -5, 6, -5, 5, -6, 5, -5, 6, -5
-11, 10, -11, 11, -10, 11, -11, 10, -11, 11, -10, 11, -11, 10, -11
21, -21, 22, -21, 21, -22, 21, -21, 22, -21, 21, -22, 21, -21, 22

Cf. A167617 (antidiagonal sums).

A131531 := proc(n) op((n mod 6)+1,[0,0,1,0,0,-1]) ; end proc:
A167613 := proc(n,k) option remember; if n= 0 then A131531(k); else procname(n-1,k+1)-procname(n-1,k) ; end if;end proc: # R. J. Mathar, Dec 17 2010

nmax = 13;
A131531 = Table[{0, 0, 1, 0, 0, -1}, {nmax}] // Flatten;
T[n_] := T[n] = Differences[A131531, n];
T[n_, k_] := T[n][[k]];
Table[T[n-k, k], {n, 1, nmax}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Oct 20 2023 *)

T(0,k) = A131531(k). T(n,k) = T(n-1,k+1) - T(n-1,k), n > 0.
T(n,n) = A001045(n). T(n,n+1) = -A001045(n). T(n,n+2) = A078008(n).
T(n,0) = -T(n,3) = (-1)^(n+1)*A024495(n).
T(n,1) = (-1)^(n+1)*A131708(n).
T(n,2) = (-1)^n*A024493(n).
T(n,k+6) = T(n,k).
a(n) = A131708(0), -A024495(0,1), A024493(0,1,2), -A131708(0,1,2,3), A024495(0,1,2,3,4), -A024493(0,1,2,3,4,5).

A242563 a(n) = 2a(n-1) - a(n-3) + 2a(n-4), a(0)=a(1)=0, a(2)=2, a(3)=3.

Original entry on oeis.org

0, 0, 2, 3, 6, 10, 21, 42, 86, 171, 342, 682, 1365, 2730, 5462, 10923, 21846, 43690, 87381, 174762, 349526, 699051, 1398102, 2796202, 5592405, 11184810, 22369622, 44739243, 89478486, 178956970, 357913941, 715827882, 1431655766, 2863311531, 5726623062, 11453246122

Offset: 0

Paul Curtz, May 17 2014

Generally, a(n) is an autosequence if its inverse binomial transform is (-1)^n*a(n). It is of the first kind if the main diagonal is 0's and the first two upper diagonals (just above the main one) are the same. It is of the second kind if the main diagonal is equal to the first upper diagonal multiplied by 2. If the first upper diagonal is an autosequence, the sequence is a super autosequence. Example: A113405. The first upper diagonal is A001045(n). Another super autosequence: 0, 0, 0 followed by A059633(n). The first upper diagonal is A000045(n).
Difference table of a(n):
   0,  0,  2, 3, 6, 10, 21, 42, ...
   0,  2,  1, 3, 4, 11, 21, 44, ...
   2, -1,  2, 1, 7, 10, 23, 41, ...
  -3,  3, -1, 6, 3, 13, 18, 45, ... .
This is an autosequence of the second kind. The main diagonal is 2*A001045(n) = A078008(n). More precisely it is a super autosequence, companion of A113405(n).
a(n+1) mod 10 = period 12: repeat 0, 2, 3, 6, 0, 1, 2, 6, 1, 2, 2, 5.
It is shifted A081374(n+1) mod 10 =
    period 12: repeat 1, 2, 2, 5, 0, 2, 3, 6, 0, 1, 2, 6.
a(n) mod 9 = period 18:
repeat 0, 0, 2, 3, 6, 1, 3, 6, 5, 0, 0, 7, 6, 3, 8, 6, 3, 4 = c(n).
c(n) + c(n+9) = 0, 0, 9, 9, 9, 9, 9, 9, 9.

			G.f. = 2*x^2 + 3*x^3 + 6*x^4 + 10*x^5 + 21*x^6 + 42*x^7 + 86*x^8 + ...

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,0,-1,2).

Cf. A000032, 1/(n+1), A164555/A027642 (all autosequences of 2nd kind). A007283, A175805.

a[n_] := (m = Mod[n, 6]; 1/3*(2^n + (-1)^n + 1/120*(m-6)*(m+1)*(m^3-29*m+40))); Table[a[n], {n, 0, 35}] (* Jean-François Alcover, May 19 2014, a non-recursive formula, after Mathematica's RSolve *)
LinearRecurrence[{2, 0, -1, 2}, {0, 0, 2, 3},50] (* G. C. Greubel, Feb 21 2017 *)

concat([0,0], Vec(x^2*(x-2)/((x+1)*(2*x-1)*(x^2-x+1)) + O(x^100))) \\ Colin Barker, May 18 2014

a(n+3) = 3*2^n - a(n), a(0)=a(1)=0, a(2)=2.
a(n) = 2*A113405(n+1) - A113405(n).
a(n+1) = 2*a(n) + period 6: repeat 0, 2, -1, 0, -2, 1. a(0)=0.
a(n) = 2^n - A081374(n+1).
a(n+3) = a(n+1) + A130755(n).
G.f.: x^2*(x-2) / ((x+1)*(2*x-1)*(x^2-x+1)). - Colin Barker, May 18 2014
a(n) = A024495(n) + A131531(n).
a(n+6) = a(n) + 21*2^n, a(0)=a(1)=0, a(2)=2, a(3)=3, a(4)=6, a(5)=10.
a(n) = A001045(n) - A092220(n).
a(n+12) = a(n) + 1365*2^n. First 12 values in the Data. (A024495(n+12) = A024495(n) + 1365*2^n).
a(3n)   = A132805(n) = 3*A015565(n).
a(3n+1) = A132804(n) = 6*A015565(n).
a(3n+2) = A132397(n) = 2*A082311(n).
a(n) = 1/3*((-1)^n - 2*cos((n*Pi)/3) + 2^n). - Alexander R. Povolotsky,  Jun 02 2014

More terms from Colin Barker, May 18 2014

A256232 Multiplicative with a(2^e) = 1-e, a(3^e) = 1, a(p^e) = e+1 if p>3.

Original entry on oeis.org

1, 0, 1, -1, 2, 0, 2, -2, 1, 0, 2, -1, 2, 0, 2, -3, 2, 0, 2, -2, 2, 0, 2, -2, 3, 0, 1, -2, 2, 0, 2, -4, 2, 0, 4, -1, 2, 0, 2, -4, 2, 0, 2, -2, 2, 0, 2, -3, 3, 0, 2, -2, 2, 0, 4, -4, 2, 0, 2, -2, 2, 0, 2, -5, 4, 0, 2, -2, 2, 0, 2, -2, 2, 0, 3, -2, 4, 0, 2, -6

Offset: 1

Michael Somos, Mar 19 2015

			G.f. = x + x^3 - x^4 + 2*x^5 + 2*x^7 - 2*x^8 + x^9 + 2*x^11 - x^12 + ...

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A099751.

Cf. A027748, A124010, A092220.

a099751 n = product $ zipWith f (a027748_row n) (a124010_row n)
   where f 2 e = e - 1; f 3 e = 1; f _ e = e + 1
-- Reinhard Zumkeller, Mar 20 2015

a[ n_] := If[ n < 1, 0, Sum[ KroneckerSymbol[ -3, d] (-1)^Quotient[ d, 3], {d, Divisors@n}]];
a[ n_] := SeriesCoefficient[ Sum[ (x^k - x^(2*k)) / (1 + x^(3*k)), {k, n}], {x, 0, n}];

{a(n) = if( n<1, 0, sumdiv( n, d, (-1)^(d\3) * kronecker( -3, d)))};

Moebius transform is period 6 sequence [1, -1, 0, -1, 1, 0, ...].
G.f.: Sum_{k>0} x^k / (1 + x^k) * Kronecker(9, k).
G.f.: Sum_{k>0} x^k / (1 - x^k) * (-1)^floor(k/3) * Kronecker(-3, k).
G.f.: Sum_{k>0} x^k / (1 - (-x)^k) * (-1)^(k mod 4 = 0) * (k mod 3 > 0).
G.f.: Sum_{k>0} (x^k - x^(2*k)) / (1 + x^(3*k)).
G.f.: Sum_{k>0} (x^k + x^(2*k)) / (1 - x^(3*k)) * (-1)^(k-1).
a(n) = (-1)^(n mod 4 = 0) * A099751(n).
From Amiram Eldar, Nov 30 2022: (Start)
Dirichlet g.f.: zeta(s)^2*(1 - 2^(1-s))*(1 - 1/3^s).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log(2)/3 = 0.462098... . (End)
a(n) = Sum_{d|n} A092220(d). - Ridouane Oudra, Sep 29 2024

A135259 a(n) = 3*A131666(n) - A131666(n+1).

Original entry on oeis.org

0, -1, 2, 1, 3, 2, 7, 13, 30, 57, 115, 226, 455, 909, 1822, 3641, 7283, 14562, 29127, 58253, 116510, 233017, 466035, 932066, 1864135, 3728269, 7456542, 14913081, 29826163, 59652322, 119304647, 238609293, 477218590, 954437177, 1908874355, 3817748706

Offset: 0

Paul Curtz, Dec 01 2007

sign

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,0,-1,2).

Cf. A131666.

a:=[0,-1,2,1];; for n in [5..35] do a[n]:=2*a[n-1]-a[n-3]+2*a[n-4]; od; a; # G. C. Greubel, Nov 21 2019

R:=PowerSeriesRing(Integers(), 35); [0] cat Coefficients(R!( x*(1-x)*(1-3*x)/((2*x-1)*(x+1)*(1-x+x^2)) )); // G. C. Greubel, Nov 21 2019

seq(coeff(series(x*(1-x)*(1-3*x)/((2*x-1)*(x+1)*(1-x+x^2)), x, n+1), x, n), n = 0 .. 35); # G. C. Greubel, Nov 21 2019

LinearRecurrence[{2,0,-1,2}, {0,-1,2,1}, 35] (* G. C. Greubel, Oct 05 2016 *)

concat(0, Vec(x*(1-x)*(1-3*x)/((2*x-1)*(x+1)*(1-x+x^2)) + O(x^35))) \\ Michel Marcus, Oct 05 2016

def A135259_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P(x*(1-x)*(1-3*x)/((2*x-1)*(x+1)*(1-x+x^2))).list()
A135259_list(35) # G. C. Greubel, Nov 21 2019

A131666(n) - a(n) = A092220(n).
O.g.f.: x*(1-x)*(1 -3*x)/( (2*x-1)*(x+1)*(1 -x +x^2) ). - R. J. Mathar, Jul 22 2008
a(n) = 2*a(n-1) - a(n-3) + 2*a(n-4). - G. C. Greubel, Oct 05 2016

Edited and extended by R. J. Mathar, Jul 22 2008

A328881 a(n+3) = 2^n - a(n), a(0)=a(2)=1, a(1)=0 for n >= 0.

Original entry on oeis.org

1, 0, 1, 0, 2, 3, 8, 14, 29, 56, 114, 227, 456, 910, 1821, 3640, 7282, 14563, 29128, 58254, 116509, 233016, 466034, 932067, 1864136, 3728270, 7456541, 14913080, 29826162, 59652323, 119304648, 238609294, 477218589, 954437176, 1908874354, 3817748707

Offset: 0

Paul Curtz, Oct 29 2019

The array of a(n) and its repeated differences:
    1,   0,   1,   0,   2,   3,   8,  14, ...
   -1,   1,  -1,   2,   1,   5,   6,  15, ...
    2,  -2,   3,  -1,   4,   1,   9,  12, ...
   -4,   5,  -4,   5,  -3,   8,   3,  19, ...
    9,  -9,   9,  -8,  11,  -5,  16,   5, ...
  -18,  18, -17,  19, -16,  21, -11,  32, ...
   36, -35,  36, -35,  37, -32,  43, -21, ...
  -71,  71, -71,  72, -69,  75, -64,  85, ...
  ...
The recurrence is the same for every row.
From Jean-François Alcover, Nov 28 2019: (Start)
It appears that, when odd, a(n) is never a multiple of 5.
Main and 3rd upper diagonals of the difference array are A001045 (Jacobsthal numbers); first upper diagonal is negated A001045; second upper diagonal is A000079 (powers of 2); 4th upper diagonal is A062092.
(End)

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,0,-1,2).

Cf. A024495, A062092, A131714.

Cf. A015565, A092220, A113405.

a[0] = a[2] = 1; a[1] = 0; a[n_] := a[n] = 2^(n - 3) - a[n - 3]; Array[a, 36, 0] (* Amiram Eldar, Nov 06 2019 *)

Vec((1 - 2*x + x^2 - x^3) / ((1 + x)*(1 - 2*x)*(1 - x + x^2)) + O(x^40)) \\ Colin Barker, Oct 29 2019

a(n+1) - 2*a(n) = period 6: repeat [-2, 1, -2, 2, -1, 2].
a(n+12) - a(n) = 455*2^n.
From Colin Barker, Oct 29 2019: (Start)
G.f.: (1 - 2*x + x^2 - x^3) / ((1 + x)*(1 - 2*x)*(1 - x + x^2)).
a(n) = 2*a(n-1) - a(n-3) + 2*a(n-4) for n>3.
(End)
a(n+2) - a(n) = A024495(n).
a(n+6) - a(n) = 7*2^n.
a(n+9) + a(n) = 57*2^n.
a(n) = A113405(n) + A092220(n+5).
9*a(n) = 2^n + 5*(-1)^n + 3*A010892(n). - R. J. Mathar, Nov 28 2019

cp's OEIS Frontend

A131531 Period 6: repeat [0, 0, 1, 0, 0, -1].

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A112465 Riordan array (1/(1+x), x/(1-x)).

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A131666 First differences of (A113405 prefixed with a 0).

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A167613 Array T(n,k) read by antidiagonals: the k-th term of the n-th difference of A131531.

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A242563 a(n) = 2*a(n-1) - a(n-3) + 2*a(n-4), a(0)=a(1)=0, a(2)=2, a(3)=3.

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A256232 Multiplicative with a(2^e) = 1-e, a(3^e) = 1, a(p^e) = e+1 if p>3.

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A135259 a(n) = 3*A131666(n) - A131666(n+1).

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A242563 a(n) = 2a(n-1) - a(n-3) + 2a(n-4), a(0)=a(1)=0, a(2)=2, a(3)=3.