A094686 -id:A094686 - cp's OEIS frontend

A291382 p-INVERT of (1,1,0,0,0,0,...), where p(S) = 1 - 2 S - S^2.

2, 7, 22, 70, 222, 705, 2238, 7105, 22556, 71608, 227332, 721705, 2291178, 7273743, 23091762, 73308814, 232731578, 738846865, 2345597854, 7446508273, 23640235416, 75050038224, 238259397096, 756395887969, 2401310279090, 7623377054503, 24201736119310

Offset: 0

Clark Kimberling, Sep 04 2017

Suppose s = (c(0), c(1), c(2), ...) is a sequence and p(S) is a polynomial. Let S(x) = c(0)*x + c(1)*x^2 + c(2)*x^3 + ... and T(x) = (-p(0) + 1/p(S(x)))/x. The p-INVERT of s is the sequence t(s) of coefficients in the Maclaurin series for T(x). Taking p(S) = 1 - S gives the "INVERT" transform of s, so that p-INVERT is a generalization of the "INVERT" transform (e.g., A033453).
In the following guide to p-INVERT sequences using s = (1,1,0,0,0,...) = A019590, in some cases t(1,1,0,0,0,...) is a shifted version of the cited sequence:
p(S)                     t(1,1,0,0,0,...)
1 - S                       A000045 (Fibonacci numbers)
1 - S^2                     A094686
1 - S^3                     A115055
1 - S^4                     A291379
1 - S^5                     A281380
1 - S^6                     A281381
1 - 2 S                     A002605
1 - 3 S                     A125145
(1 - S)^2                   A001629
(1 - S)^3                   A001628
(1 - S)^4                   A001629
(1 - S)^5                   A001873
(1 - S)^6                   A001874
1 - S - S^2                 A123392
1 - 2 S - S^2               A291382
1 - S - 2 S^2               A124861
1 - 2 S - S^2               A291383
(1 - 2 S)^2                 A073388
(1 - 3 S)^2                 A291387
(1 - 5 S)^2                 A291389
(1 - 6 S)^2                 A291391
(1 - S)(1 - 2 S)            A291393
(1 - S)(1 - 3 S)            A291394
(1 - 2 S)(1 - 3 S)          A291395
(1 - S)(1 - 2 S)            A291393
(1 - S)(1 - 2 S)(1 - 3 S)   A291396
1 - S - S^3                 A291397
1 - S^2 - S^3               A291398
1 - S - S^2 - S^3           A186812
1 - S - S^2 - S^3 - S^4     A291399
1 - S^2 - S^4               A291400
1 - S - S^4                 A291401
1 - S^3 - S^4               A291402
1 - 2 S^2 - S^4             A291403
1 - S^2 - 2 S^4             A291404
1 - 2 S^2 - 2 S^4           A291405
1 - S^3 - S^6               A291407
(1 - S)(1 - S^2)            A291408
(1 - S^2)(1 - S)^2          A291409
1 - S - S^2 - 2 S^3         A291410
1 - 2 S - S^2 + S^3         A291411
1 - S - 2 S^2 + S^3         A291412
1 - 3 S + S^2 + S^3         A291413
1 - 2 S + S^3               A291414
1 - 3 S + S^2               A291415
1 - 4 S + S^2               A291416
1 - 4 S + 2 S^2             A291417

Clark Kimberling, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2, 3, 2, 1)

Cf. A019590, A290890, A291000, A291219, A291728, A292479, A292480.

z = 60; s = x + x^2; p = 1 - 2 s - s^2;
Drop[CoefficientList[Series[s, {x, 0, z}], x], 1]  (* A019590 *)
Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1]  (* A291382 *)

G.f.: (-2 - 3 x - 2 x^2 - x^3)/(-1 + 2 x + 3 x^2 + 2 x^3 + x^4).

a(n) = 2*a(n-1) + 3*a(n-2) + 2*a(n-3) + a(n-4) for n >= 5.

A079962 Number of permutations satisfying -k <= p(i) - i <= r and p(i) - i not in I, i=1..n, with k=1, r=5, I={1,3}.

Original entry on oeis.org

1, 1, 1, 2, 3, 5, 9, 14, 22, 36, 58, 94, 153, 247, 399, 646, 1045, 1691, 2737, 4428, 7164, 11592, 18756, 30348, 49105, 79453, 128557, 208010, 336567, 544577, 881145, 1425722, 2306866, 3732588, 6039454, 9772042, 15811497, 25583539, 41395035

Offset: 0

Vladimir Baltic, Feb 19 2003

Number of compositions (ordered partitions) of n into elements of the set {1,3,5,6}. - Mark Dols, Aug 20 2010

D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), pp. 755-770. North-Holland, Amsterdam, 1970.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (2010), 119-135
Index entries for linear recurrences with constant coefficients, signature (1,0,1,0,1,1).

Cf. A002524, A002525, A002526, A002527, A002528, A002529, A072827, A072850, A072851, A072852, A072853, A072854, A072855, A072856, A079955 - A080014.

[Round(Fibonacci(n+3)/4): n in [0..40]]; // G. C. Greubel, Jan 21 2022

with(combinat,fibonacci): seq(round(fibonacci(n+3)/4),n=0..38) # Mircea Merca, Jan 04 2011

LinearRecurrence[{1,0,1,0,1,1}, {1,1,1,2,3,5}, 41] (* G. C. Greubel, Jan 21 2022 *)

a(n)=fibonacci(n+3)\/4 \\ Charles R Greathouse IV, Oct 07 2015

[(1/4)*(fibonacci(n+3) + chebyshev_U(n,1/2) + chebyshev_U(2*n,1/2)) for n in (0..40)] # G. C. Greubel, Jan 21 2022

a(n) = a(n-1) + a(n-3) + a(n-5) + a(n-6).
G.f.: 1/((1+x+x^2)*(1-x+x^2)*(1-x-x^2)).
a(n+1)/a(n) -> golden ratio A001622. - Roger L. Bagula, Mar 13 2006
a(n) + a(n+2) + a(n+4) = Fibonacci(n+5). - Mark Dols, Aug 20 2010
a(n) = round(Fibonacci(n+3)/4). - Mircea Merca, Jan 04 2011
a(n+6) - a(n) = A000045(n+6). - Paul Curtz, Jun 29 2013
a(n) + a(n+1) + a(n+2) = A024490(n+6). - R. J. Mathar, Jun 30 2013
a(n) - a(n-1) + a(n-2) = A094686(n). - R. J. Mathar, Jun 30 2013
4*a(n) = A057078(n) + A010892(n) + A000045(n+3). - R. J. Mathar, Nov 02 2016

A093040 Expansion of (1+x)/((1+x+x^2)(1-x-x^2)).

Original entry on oeis.org

1, 1, 1, 3, 4, 6, 11, 17, 27, 45, 72, 116, 189, 305, 493, 799, 1292, 2090, 3383, 5473, 8855, 14329, 23184, 37512, 60697, 98209, 158905, 257115, 416020, 673134, 1089155, 1762289, 2851443, 4613733, 7465176, 12078908, 19544085, 31622993, 51167077

Offset: 0

Paul Barry, Mar 15 2004

The sequence 0,1,1,1,3... has a(n) = Fib(n+1)/2-A049347(n)/2. It counts paths of length n between two of the vertices of the graph with adjacency matrix [0,1,0,0;0,0,1,1;1,1,0,0;0,0,1,0].
Diagonal sums of Riordan array ((1+x), x(1+x)^2). - Paul Barry, May 31 2006
a(n) is the number of compositions of n into parts 1,2,3 with no two consecutive 1's.  For example a(5) = 6 because we have: 3+2, 2+3, 1+3+1, 2+2+1, 2+1+2, 1+2+2. - Geoffrey Critzer, Mar 15 2014
a(n) is the number of compositions of n+1 into an odd number of parts 1 and 2, that is, the number of barcodes of width n+1 with alternating black and white bars of width 1 or 2 and black border (see the first recurrence formula). - Grégoire Nicollier, Apr 04 2022

			G.f. = 1 + x + x^2 + 3*x^3 + 4*x^4 + 6*x^5 + 11*x^6 + 17*x^7 + 27*x^8 + 45*x^9 + ...

MacKay, Information Theory, Inference and Learning Algorithms, CUP, 2003, p. 251

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Levi Axelrod, Nathan Bickel, Anastasia Halfpap, Luke Hawranick, Alex Parker, and Cole Swain, Statistics of maximal independent sets in grid-like graphs, arXiv:2506.22317 [math.CO], 2025. See p. 20.
Joshua P. Bowman, Compositions with an Odd Number of Parts, and Other Congruences, J. Int. Seq (2024) Vol. 27, Art. 24.3.6. See p. 19.
David Broadhurst, Multiple Deligne values: a data mine with empirically tamed denominators, arXiv:1409.7204 [hep-th], 2014. See p. 10.
Leonard Rozendaal, Pisano word, tesselation, plane-filling fractal, Preprint, 2017.
Alexander Stoimenow, Generating Functions, Fibonacci Numbers and Rational Knots, arXiv:math/0210174 [math.GT], 2002.
Index entries for linear recurrences with constant coefficients, signature (0,1,2,1).

Cf. A005252, A057078.

[Floor(Fibonacci(n+3)/2)-Floor(Fibonacci(n+1)/2): n in [1..50]]; // Vincenzo Librandi, Jul 10 2012

CoefficientList[Series[((1+x)/(1-x-x^2)+(1-x^2)/(1-x^3))/2,{x,0,50}],x] (* Vincenzo Librandi, Jul 10 2012 *)
a[ n_] := SeriesCoefficient[ If[ n < 0, x^3 (1 + x) / (1 + 2 x + x^2 - x^4), (1 + x) / (1 - x^2 - 2 x^3 - x^4)], {x, 0, Abs@n}]; (* Michael Somos, Mar 19 2014 *)
LinearRecurrence[{0, 1, 2, 1}, {1, 1, 1, 3}, 39] (* Jean-François Alcover, Sep 21 2017 *)

Vec(((1+x)/(1-x-x^2)+(1-x^2)/(1-x^3))/2 + O(x^50)) \\ Michel Marcus, Sep 27 2014

G.f.: ((1+x)/(1-x-x^2)+(1-x^2)/(1-x^3))/2.
a(n) = a(n-2) + 2*a(n-3) + a(n-4).
a(n) = Fib(n+2)/2+sqrt(3)sin(2*Pi*n/3+Pi/3)/3 = Fib(n+2)/2+A057078(n)/2.
a(n-1) = Sum_{k=0..floor(n/2)} if(mod(n-k, 2)=1, binomial(n-k, k), 0).
a(n-1) = A094686(n) - Fib(n). - Paul Barry, Jan 13 2005
a(n) = Sum_{k=0..floor(n/2)} binomial(2k+1,n-2k). - Paul Barry, May 31 2006
a(n) = floor(Fibonacci(n+3)/2) - floor(Fibonacci(n+1)/2). - Gary Detlefs, Mar 13 2011
a(n) = a(n-2) + 2*a(n-3) + a(n-4), a(-3-n) = (-1)^n * A005252(n) for all n in Z. - Michael Somos, Mar 19 2014
a(n-1) + 2*a(n) - a(n+2) = a(n) - a(n-1) - a(n-2) = A057078(n) for all n in Z. - Michael Somos, Mar 19 2014
2*a(n) = A057078(n) + A000045(n+2). - R. J. Mathar, Sep 16 2017

A113067 Expansion of -x/((x^2+x+1)(x^2+3x+1)); invert transform gives signed version of tetrahedral numbers A000292.

Original entry on oeis.org

0, -1, 4, -11, 28, -72, 188, -493, 1292, -3383, 8856, -23184, 60696, -158905, 416020, -1089155, 2851444, -7465176, 19544084, -51167077, 133957148, -350704367, 918155952, -2403763488, 6293134512, -16475640049, 43133785636, -112925716859, 295643364940, -774004377960

Offset: 0

Creighton Dement, Oct 13 2005

Invert(a(n)) gives (0, -1, 4, -10, 20, -35, ...) = A000292 (with alternating signs).
Binomial(a(n)) gives (0, -1, 2, -2, 4, -7, 10, ...) = A094686 (with alternating signs, from 2nd term).
Floretion Algebra Multiplication Program, FAMP Code: 2basei[C*F]; C = - .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki'; F = + .5'i + .5'ii' + .5'ij' + .5'ik'

Creighton Dement, Floretion Integer Sequences (work in progress).

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (-4,-5,-4,-1).

Cf. A000292, A113067, A113068, A094686, A001906, A109961, A290890.

-x/((x^2+x+1)*(x^2+3*x+1)) + O[x]^30 // CoefficientList[#, x]& (* Jean-François Alcover, Jun 15 2017 *)

concat(0, Vec(-x / ((1 + x + x^2)*(1 + 3*x + x^2)) + O(x^30))) \\ Colin Barker, May 11 2019

[((lucas_number1(n,3,1)-lucas_number1(n,1,1)))/(-2) for n in range(1,32)] # Zerinvary Lajos, Jul 06 2008

a(n) + a(n+1) + a(n+2) = (-1)^n *A001906(n+2) = (-1)^n*F(2n+4).
a(n) + 3*a(n+1) + 3*a(n+2) + a(n+3) = ((-1)^(n+1))*A109961(n+2).
(|a(n)|) = A290890(n) for n >= 0, this being the p-INVERT of (1,2,3,4,...), where p(S) = 1 - S^2.  - Clark Kimberling, Aug 21 2017
a(n) = -4*a(n-1) - 5*a(n-2) - 4*a(n-3) - a(n-4) for n > 3. - Colin Barker, May 11 2019
2*a(n) = (-1)^n*A001906(n+1) - A049347(n). - R. J. Mathar, Sep 20 2020

A116088 Riordan array (1, x*(1+x)^2).

Original entry on oeis.org

1, 0, 1, 0, 2, 1, 0, 1, 4, 1, 0, 0, 6, 6, 1, 0, 0, 4, 15, 8, 1, 0, 0, 1, 20, 28, 10, 1, 0, 0, 0, 15, 56, 45, 12, 1, 0, 0, 0, 6, 70, 120, 66, 14, 1, 0, 0, 0, 1, 56, 210, 220, 91, 16, 1, 0, 0, 0, 0, 28, 252, 495, 364, 120, 18, 1

Offset: 0

Paul Barry, Feb 04 2006

			Triangle begins as:
  1;
  0, 1;
  0, 2, 1;
  0, 1, 4,  1;
  0, 0, 6,  6,  1;
  0, 0, 4, 15,  8,  1;
  0, 0, 1, 20, 28, 10,  1;
  0, 0, 0, 15, 56, 45, 12, 1;

Michael De Vlieger, Table of n, a(n) for n = 0..11475 (Rows 0 <= n <= 150).
Milan Janjić, Pascal Matrices and Restricted Words, J. Int. Seq., Vol. 21 (2018), Article 18.5.2.

Row sums are A002478. Diagonal sums are A094686. Inverse is (-1)^(n-k) * A109971(n,k). Unsigned version of A109970.

Flat(List([0..10], n->List([0..n], k-> Binomial(2*k, n-k) ))); # G. C. Greubel, May 09 2019

[[Binomial(2*k, n-k): k in [0..n]]: n in [0..10]]; // G. C. Greubel, May 09 2019

Flatten[Table[Binomial[2k,n-k],{n,0,20},{k,0,n}]] (* Harvey P. Dale, Oct 22 2012 *)

{T(n,k) = binomial(2*k, n-k)}; \\ G. C. Greubel, May 09 2019

[[binomial(2*k, n-k) for k in (0..n)] for n in (0..10)] # G. C. Greubel, May 09 2019

G.f.: 1/(1-x*y*(1+x)^2).

Number triangle T(n,k) = C(2*k, n-k) = C(n,k)*C(3*k,n)/C(3*k,k).

A109970 Riordan array (1,x(1-x)^2).

Original entry on oeis.org

1, 0, 1, 0, -2, 1, 0, 1, -4, 1, 0, 0, 6, -6, 1, 0, 0, -4, 15, -8, 1, 0, 0, 1, -20, 28, -10, 1, 0, 0, 0, 15, -56, 45, -12, 1, 0, 0, 0, -6, 70, -120, 66, -14, 1, 0, 0, 0, 1, -56, 210, -220, 91, -16, 1, 0, 0, 0, 0, 28, -252, 495, -364, 120, -18, 1

Offset: 0

Paul Barry, Jul 06 2005

Row sums are A077954. Diagonal sums are (-1)^n*A094686(n). Matrix inverse is A109971.

			Rows begin
1;
0,1;
0,-2,1;
0,1,-4,1;
0,0,6,-6,1;
0,0,-4,15,-8,1;
0,0,1,-20,28,-10,1;
0,0,0,15,-56,45,-12,1;

G.f.: 1/(1-xy(1-x)^2); Number triangle T(n, k)=binomial(2k, n-k)*(-1)^(n-k).

A113726 A Jacobsthal convolution.

Original entry on oeis.org

1, 0, 1, 4, 5, 8, 25, 44, 77, 176, 353, 660, 1365, 2776, 5417, 10876, 21981, 43648, 87153, 175076, 349669, 698280, 1398585, 2797260, 5590381, 11184720, 22373761, 44735284, 89474165, 178969208, 357910345, 715807004, 1431683837, 2863325216

Offset: 0

Paul Barry, Nov 08 2005

Convolution of A001045(n+1) and A001607(n+1).

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,1,4,4).

Cf. A094686, A089977, A001045, A001607.

LinearRecurrence[{0,1,4,4},{1,0,1,4},40] (* Harvey P. Dale, Apr 30 2025 *)

G.f.: 1/((1-x-2*x^2)*(1+x+2*x^2)).
a(n) = a(n-2) + 4*a(n-3) + 4*a(n-4).
a(n) = Sum_{k=0..floor(n/2)} C(n-k, k)*2^k*(1+(-1)^(n-k))/2.
a(n) = 2^n/3 + (-1)^n/6 + A001607(n+1)/2. - R. J. Mathar, Aug 23 2011
a(n) = sum(A128099(n, n-2*k), k=0..floor(n/2)). - Johannes W. Meijer, Aug 28 2013

A283834 Number of length-n binary vectors beginning with 0, ending with 1, and avoiding 4 consecutive 0's and 4 consecutive 1's.

Original entry on oeis.org

1, 0, 1, 2, 4, 6, 12, 22, 41, 74, 137, 252, 464, 852, 1568, 2884, 5305, 9756, 17945, 33006, 60708, 111658, 205372, 377738, 694769, 1277878, 2350385, 4323032, 7951296, 14624712, 26899040, 49475048, 90998801, 167372888, 307846737, 566218426, 1041438052

Offset: 0

N. J. A. Sloane, Mar 25 2017

Alois P. Heinz, Table of n, a(n) for n = 0..1000
Stefano Bilotta, Variable-length Non-overlapping Codes, arXiv preprint arXiv:1605.03785 [cs.IT], 2016 [See Table 2].
Index entries for linear recurrences with constant coefficients, signature (0,1,2,3,2,1).

Cf. A000073, A094686, A283835, A283836, A283837, A283838.

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/((1+x)*(1+x^2)*(1-x-x^2-x^3)) )); // G. C. Greubel, Feb 09 2023

CoefficientList[Series[1/((1+x)*(1+x^2)*(1-x-x^2-x^3)), {x,0,50}], x] (* Indranil Ghosh, Mar 26 2017 *)

Vec(1/((1+x)*(1+x^2)*(1-x-x^2-x^3)) + O(x^50)) \\ Indranil Ghosh, Mar 26 2017

@CachedFunction
def b(n): # b = A000073
    if (n<3): return (0,0,1)[n]
    else: return b(n-1) + b(n-2) + b(n-3)
def A283834(n): return (1/4)*((-1)^n +i^n*((n+1)%2) -i^(n+3)*(n%2) +2*b(n+2))
[A283834(n) for n in range(41)] # G. C. Greubel, Feb 09 2023

G.f.: 1/((1+x)*(1+x^2)*(1-x-x^2-x^3)). - Alois P. Heinz, Mar 25 2017

a(n) = (1/4)*((-1)^n + i^n*(n+1 mod 2) - i^(n+3)*(n mod 2) + 2*A000073(n+2)). - G. C. Greubel, Feb 09 2023

More terms from Alois P. Heinz, Mar 25 2017

A283838 Irregular triangle read by rows: T(n,k) (n >= 8, 3 <= k <= floor(n/2)-1) = number of binary vectors of length <= n that start with 1^k, 0, end with 1, 0^k, and the factor between 1^k and 0^k does not contain 0^k or 1^k.

Original entry on oeis.org

1, 3, 5, 1, 9, 3, 16, 7, 1, 26, 13, 3, 43, 25, 7, 1, 71, 47, 15, 3, 115, 88, 29, 7, 1, 187, 162, 57, 15, 3, 304, 299, 111, 31, 7, 1, 492, 551, 215, 61, 15, 3, 797, 1015, 416, 121, 31, 7, 1, 1291, 1867, 802, 239, 63, 15, 3, 2089, 3435, 1547, 471, 125, 31, 7, 1, 3381, 6319, 2983, 927, 249, 63, 15, 3

Offset: 8

N. J. A. Sloane, Mar 25 2017

			Triangle begins:
     1,
     3,
     5,     1,
     9,     3,
    16,     7,    1,
    26,    13,    3,
    43,    25,    7,    1,
    71,    47,   15,    3,
   115,    88,   29,    7,   1,
   187,   162,   57,   15,   3,
   304,   299,  111,   31,   7,   1,
   492,   551,  215,   61,  15,   3,
   797,  1015,  416,  121,  31,   7,  1,
  1291,  1867,  802,  239,  63,  15,  3,
  2089,  3435, 1547,  471, 125,  31,  7, 1,
  3381,  6319, 2983,  927, 249,  63, 15, 3,
  5472, 11624, 5751, 1824, 495, 127, 31, 7, 1,
  ...

Alois P. Heinz, Rows n = 8..290, flattened
Stefano Bilotta, Variable-length Non-overlapping Codes, arXiv preprint arXiv:1605.03785 [cs.IT], 2016 [See Table 3].

Cf. A094686, A283834-A283837.

For row sums see A283839.

gf[k_] := x^(2k)(x-x^k)^2 / ((1-x)(1-x^k)(1-2x+x^k));
T[n_, k_] := SeriesCoefficient[gf[k], {x, 0, n}];
Table[T[n, k], {n, 8, 24}, {k, 3, Floor[n/2]-1}] // Flatten (* Jean-François Alcover, Apr 05 2017 *)

A124369 Riordan array (1/((1-x-x^2)(1+x+x^2)),x(1+x)/((1-x-x^2)(1+x+x^2))).

Original entry on oeis.org

1, 0, 1, 1, 1, 1, 2, 2, 2, 1, 2, 6, 4, 3, 1, 4, 9, 12, 7, 4, 1, 7, 17, 24, 21, 11, 5, 1, 10, 34, 48, 50, 34, 16, 6, 1, 17, 58, 103, 110, 91, 52, 22, 7, 1, 28, 104, 200, 250, 220, 152, 76, 29, 8, 1, 44, 188, 385, 534, 530, 400, 239, 107, 37, 9, 1

Offset: 0

Paul Barry, Oct 27 2006

Row sums are A123392. Diagonal sums are A124370. First column is A094686. Product of A026729 and abs(A049310).

			Triangle begins
1,
0, 1,
1, 1, 1,
2, 2, 2, 1,
2, 6, 4, 3, 1,
4, 9, 12, 7, 4, 1,
7, 17, 24, 21, 11, 5, 1,
10, 34, 48, 50, 34, 16, 6, 1,
17, 58, 103, 110, 91, 52, 22, 7, 1

Number triangle T(n,k)=sum{j=0..n, C(j,n-j)*C((j+k)/2,(j-k)/2)*(1+(-1)^(j-k))/2};

T(n,k) = T(n-1,k-1) + T(n-2,k) + T(n-2,k-1) + 2*T(n-3,k) + T(n-4,k), T(0,0) = 1, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Jan 22 2014

cp's OEIS Frontend

A291382 p-INVERT of (1,1,0,0,0,0,...), where p(S) = 1 - 2 S - S^2.

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A079962 Number of permutations satisfying -k <= p(i) - i <= r and p(i) - i not in I, i=1..n, with k=1, r=5, I={1,3}.

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A093040 Expansion of (1+x)/((1+x+x^2)(1-x-x^2)).

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A113067 Expansion of -x/((x^2+x+1)*(x^2+3*x+1)); invert transform gives signed version of tetrahedral numbers A000292.

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A116088 Riordan array (1, x*(1+x)^2).

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A109970 Riordan array (1,x(1-x)^2).

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A113726 A Jacobsthal convolution.

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A113067 Expansion of -x/((x^2+x+1)(x^2+3x+1)); invert transform gives signed version of tetrahedral numbers A000292.