A004275 -id:A004275 - cp's OEIS frontend

A055808 a(n) and floor(a(n)/4) are both squares; i.e., squares that remain squares when written in base 4 and last digit is removed.

0, 1, 4, 16, 36, 64, 100, 144, 196, 256, 324, 400, 484, 576, 676, 784, 900, 1024, 1156, 1296, 1444, 1600, 1764, 1936, 2116, 2304, 2500, 2704, 2916, 3136, 3364, 3600, 3844, 4096, 4356, 4624, 4900, 5184, 5476, 5776, 6084, 6400, 6724, 7056, 7396, 7744, 8100

Offset: 0

Henry Bottomley, Jul 14 2000

Let A(x) = (1 + k*x + (k-1)*x^2). Then the coefficients of (A(x))^2 sum to 4*k^2, where k = (n - 1). Examples: if k = 3 we have (1 + 3*x + 2*x^2)^2 = (1 + 6*x + 13x^2 + 12*x^3 + 4*x^4), and ( 1 + 6 + 13 + 12 + 4) = 36. If k = 4 we have (1 + 4*x + 3*x^2)^2 = (1 + 8*x + 22*x^2 + 24*x^3 + 9*x^4), and (1 + 8 + 22 + 24 + 9) = 64 = a(5). - Gary W. Adamson, Aug 02 2015

For n>0, a(n) are the Engel expansion of A197036. - Benedict W. J. Irwin, Dec 15 2016

			36 is in the sequence because 36 = 6^2 = 210 base 3 and 21 base 4 = 9 = 3^2.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A023110. Essentially A016742 with one addition.

[Floor((2*n^2)/(1 + n))^2: n in [0..60]]; // Vincenzo Librandi, Aug 03 2015

Join[{0, 1}, LinearRecurrence[{3, -3, 1}, {4, 16, 36}, 50]] (* Vincenzo Librandi, Aug 03 2015 *)

concat(0, Vec(x*(x^3-7*x^2-x-1)/(x-1)^3 + O(x^100))) \\ Colin Barker, Sep 15 2014

is_ok(n)=issquare(n) && issquare(floor(n/4));
first(m)=my(v=vector(m),r=0);for(i=1,m,while(!is_ok(r),r++);v[i]=r;r++;);v; /* Anders Hellström, Aug 08 2015 */

a(n) = A004275(n)^2. - M. F. Hasler, Jan 16 2012

a(n) = 4*(-1+n)^2 for n>1; a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>4; G.f.: x*(x^3-7*x^2-x-1) / (x-1)^3. - Colin Barker, Sep 15 2014

A091090 In binary representation: number of editing steps (delete, insert, or substitute) to transform n into n + 1.

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 6, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 6, 1, 2, 1, 3, 1, 2

Offset: 0

Reinhard Zumkeller, Dec 19 2003

Apparently, one less than the number of cyclotomic factors of the polynomial x^n - 1. - Ralf Stephan, Aug 27 2013

Let the binary expansion of n >= 1 end with m >= 0 1's. Then a(n) = m if n = 2^m-1 and a(n) = m+1 if n > 2^m-1. - Vladimir Shevelev, Aug 14 2017

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Dillan Agrawal, Selena Ge, Jate Greene, Tanya Khovanova, Dohun Kim, Rajarshi Mandal, Tanish Parida, Anirudh Pulugurtha, Gordon Redwine, Soham Samanta, and Albert Xu, Chip-Firing on Infinite k-ary Trees, arXiv:2501.06675 [math.CO], 2025. See p. 11.
Michael Gilleland, Levenshtein Distance [broken link] [It has been suggested that this algorithm gives incorrect results sometimes. - _N. J. A. Sloane_]
Ryota Inagaki, Tanya Khovanova, and Austin Luo, On Chip-Firing on Undirected Binary Trees, Ann. Comb. (2025). See p. 22.
Frank Ruskey and Chris Deugau, The Combinatorics of Certain k-ary Meta-Fibonacci Sequences, JIS 12 (2009), Article 09.4.3.
Vladimir Shevelev, On a Luschny question, arXiv:1708.08096 [math.NT], 2017.
Eric Weisstein's World of Mathematics, Binary.
Eric Weisstein's World of Mathematics, Binary Carry Sequence.
WikiBooks: Algorithm Implementation, Levenshtein distance.
Index entries for sequences related to binary expansion of n.

Cf. A007088, A135517.

This is Guy Steele's sequence GS(2, 4) (see A135416).

a091090 n = a091090_list !! n
a091090_list = 1 : f [1,1] where f (x:y:xs) = y : f (x:xs ++ [x,x+y])
-- Same list generator function as for a036987_list, cf. A036987.
-- Reinhard Zumkeller, Mar 13 2011

a091090' n = levenshtein (show $ a007088 (n + 1)) (show $ a007088 n) where
  levenshtein :: (Eq t) => [t] -> [t] -> Int
  levenshtein us vs = last $ foldl transform [0..length us] vs where
    transform xs@(x:xs') c = scanl compute (x+1) (zip3 us xs xs') where
      compute z (c', x, y) = minimum [y+1, z+1, x + fromEnum (c' /= c)]
-- Reinhard Zumkeller, Jun 09 2015

-- following Vladeta Jovovic's formula
import Data.List (transpose)
a091090'' n = vjs !! n where
   vjs = 1 : 1 : concat (transpose [[1, 1 ..], map (+ 1) $ tail vjs])
-- Reinhard Zumkeller, Jun 09 2015

A091090 := proc(n)
    if n = 0 then
        1;
    else
        A007814(n+1)+1-A036987(n) ;
    end if;
end proc:
seq(A091090(n),n=0..100); # R. J. Mathar, Sep 07 2016
# Alternatively, explaining the connection with A135517:
a := proc(n) local count, k; count := 1; k := n;
while k <> 1 and k mod 2 <> 0 do count := count + 1; k := iquo(k, 2) od:
count end: seq(a(n), n=0..101); # Peter Luschny, Aug 10 2017

a[n_] := a[n] = Which[n==0, 1, n==1, 1, EvenQ[n], 1, True, a[(n-1)/2] + 1]; Array[a, 102, 0] (* Jean-François Alcover, Aug 12 2017 *)

a(n)=my(m=valuation(n+1,2)); if(n>>m, m+1, max(m, 1)) \\ Charles R Greathouse IV, Aug 15 2017

def A091090(n): return (~(n+1)&n).bit_length()+bool(n&(n+1)) if n else 1 # Chai Wah Wu, Sep 18 2024

a(n) = LevenshteinDistance(A007088(n), A007088(n + 1)).
a(n) = A007814(n + 1) + 1 - A036987(n).
a(n) = A152487(n + 1, n). - Reinhard Zumkeller, Dec 06 2008
a(A004275(n)) = 1. - Reinhard Zumkeller, Mar 13 2011
From Vladeta Jovovic, Aug 25 2004, fixed by Reinhard Zumkeller, Jun 09 2015: (Start)
a(2*n) = 1, a(2*n + 1) = a(n) + 1 for n > 0.
G.f.: 1 + Sum_{k > 0} x^(2^k - 1)/(1 - x^(2^(k - 1))). (End)
Let T(x) be the g.f., then T(x) - x*T(x^2) = x/(1 - x). - Joerg Arndt, May 11 2010
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2. - Amiram Eldar, Sep 29 2023
a(n) = A000120(n) + A070939(n) - A000120(n+1) - A070939(n+1) + 2. - Chai Wah Wu, Sep 18 2024

A204518 Numbers such that floor(a(n)^2 / 6) is a square.

Original entry on oeis.org

0, 1, 2, 3, 5, 10, 27, 49, 98, 267, 485, 970, 2643, 4801, 9602, 26163, 47525, 95050, 258987, 470449, 940898, 2563707, 4656965, 9313930, 25378083, 46099201, 92198402, 251217123, 456335045, 912670090, 2486793147, 4517251249, 9034502498, 24616714347

Offset: 1

M. F. Hasler, Jan 15 2012

Or: Numbers whose square, with its last base-6 digit dropped, is again a square. (For the three initial terms whose square has only one digit in base 6, this is then meant to yield zero.)

Index entries for linear recurrences with constant coefficients, signature (0,0,10,0,0,-1).

Cf. A023110 (base 10), A204502 (base 9), A204514 (base 8), A204516 (base 7), A204520 (base 5), A004275 (base 4), A055793 (base 3), A055792 (base 2).

b=6;for(n=0,2e9,issquare(n^2\b) & print1(n","))

concat(0, Vec(-x^2*(x+1)*(3*x^4+7*x^3-2*x^2-x-1)/(x^6-10*x^3+1) + O(x^100))) \\ Colin Barker, Sep 18 2014

a(n) = sqrt(A055851(n)).
From Colin Barker, Sep 18 2014: (Start)
a(n) = 10*a(n-3) - a(n-6) for n > 7.
G.f.: -x^2*(x+1)*(3*x^4 + 7*x^3 - 2*x^2 - x - 1) / (x^6-10*x^3+1). (End)
a(3n+2) = A001079(n). a(3n) = A087799(n-1). - R. J. Mathar, Feb 05 2020

More terms from Colin Barker, Sep 18 2014

A204520 Numbers such that floor(a(n)^2 / 5) is a square.

Original entry on oeis.org

0, 1, 2, 3, 7, 9, 18, 47, 123, 161, 322, 843, 2207, 2889, 5778, 15127, 39603, 51841, 103682, 271443, 710647, 930249, 1860498, 4870847, 12752043, 16692641, 33385282

Offset: 1

M. F. Hasler, Jan 15 2012

nonn

Also: Numbers whose square, with its last base-5 digit dropped, is again a square. (For the three initial terms whose squares have only one digit in base 5, it is then understood that this yields zero.)

Cf. A031149, A055812, A204502, A204514, A204516, A204518 and A004275, A001075, A001541 for the analog in bases 10,...,6 and 4, 3, 2.

Select[Range[0,5*10^6],IntegerQ[Sqrt[Floor[#^2/5]]]&] (* The program generates the first 24 terms of the sequence. *) (* Harvey P. Dale, Jul 15 2025 *)

b=5;for(n=0,2e9,issquare(n^2\b) && print1(n","))

a(n) = sqrt(A055812(n)).

Empirical g.f.: -x^2*(x+1)*(3*x^6 + 4*x^5 + 14*x^4 - 5*x^3 - 2*x^2 - x-1) / ((x^4 - 4*x^2 - 1)*(x^4 + 4*x^2 - 1)). - Colin Barker, Sep 15 2014

A046698 a(0) = 0, a(1) = 1, a(n) = a(a(n-1)) + a(a(n-2)) if n > 1.

Original entry on oeis.org

0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset: 0

N. J. A. Sloane, R. K. Guy

Partial sums are A004275. Binomial transform is A048492, starting with 0. - Paul Barry, Feb 28 2003
From Elmo R. Oliveira, Jul 25 2024: (Start)
Continued fraction expansion of 2 - sqrt(2) = A101465.
Decimal expansion of 101/9000. (End)

Sequence proposed by Reg Allenby.

Ömür Deveci, Zafer Adıgüzel, and Taha Doğan, On the Generalized Fibonacci-circulant-Hurwitz numbers, Notes on Number Theory and Discrete Mathematics (2020) Vol. 26, No. 1, 179-190.
O. Deveci, Y. Akuzum, E. Karaduman, and O. Erdag, The Cyclic Groups via Bezout Matrices, Journal of Mathematics Research, Vol. 7, No. 2, 2015, pp. 34-41.
Eric Weisstein's World of Mathematics, Fibonacci n-Step Number
Index entries for linear recurrences with constant coefficients, signature (1).

Cf. A004275, A048492, A101465 (decimal expansion of 2 - sqrt(2)).

Cf. A033324, A114955, A343461.

CoefficientList[Series[x (1 + x^2)/(1 - x), {x, 0, 104}], x] (* or *)
Nest[Append[#, #[[#[[-1]] + 1]] + #[[#[[-2]] + 1 ]]] &, {0, 1}, 105] (* Michael De Vlieger, Jul 31 2020 *)

PARI
```
a(n)=(n>0)+(n>2)
```

G.f.: x*(1+x^2)/(1-x). - Paul Barry, Feb 28 2003
From Elmo R. Oliveira, Jul 25 2024: (Start)
E.g.f.: 2*exp(x) - x - 1.
a(n) = 2 for n > 2.
a(n) = 2 - A033324(n+2) = 4 - A343461(n+4) = A114955(n+6) - 6. (End)

A249982 T(n,k) is the number of length n+1 0..2k arrays with the sum of the absolute values of adjacent differences equal to nk.

Original entry on oeis.org

4, 6, 10, 8, 24, 20, 10, 42, 88, 64, 12, 64, 208, 384, 136, 14, 90, 426, 1242, 1606, 466, 16, 120, 728, 3030, 6856, 7138, 1012, 18, 154, 1178, 6252, 22560, 43068, 31380, 3580, 20, 192, 1744, 11524, 55372, 168506, 245860, 141272, 7864, 22, 234, 2508, 19574, 123154

Offset: 1

R. H. Hardin, Nov 10 2014

			Table starts:
.....4.......6........8........10.........12..........14..........16
....10......24.......42........64.........90.........120.........154
....20......88......208.......426........728........1178........1744
....64.....384.....1242......3030.......6252.......11524.......19574
...136....1606.....6856.....22560......55372......123154......237348
...466....7138....43068....168506.....508902.....1290856.....2886016
..1012...31380...245860...1293326....4598532....14027522....35380112
..3580..141272..1589346...9937894...43752328...152155572...446342246
..7864..635686..9213728..77372824..399919272..1672105528..5529256528
.28340.2890884.60568000.604180880.3872197278.18444783546.70948896558
Some solutions for n=5 k=4:
..8....5....0....8....3....7....1....0....8....1....1....1....0....0....2....4
..3....1....5....3....8....0....6....3....4....6....2....5....7....2....5....8
..8....6....3....8....0....7....3....2....8....0....6....3....1....8....7....7
..1....4....4....0....2....5....7....8....8....2....0....8....4....6....0....3
..1....8....0....1....4....3....1....1....1....0....5....2....6....0....0....0
..4....3....8....2....1....1....3....4....6....5....1....5....4....4....8....8

R. H. Hardin, Table of n, a(n) for n = 1..6839

Row 1 is A004275(n+2).

Row 2 is A067728.

Empirical for row n:
n=1: a(n) = 2*n + 2
n=2: a(n) = 2*n^2 + 8*n
n=3: a(n) = 2*a(n-1) +a(n-2) -4*a(n-3) +a(n-4) +2*a(n-5) -a(n-6); also a polynomial of degree 3 plus a quasipolynomial of degree 1 with period 2
n=4: a(n) = (14/3)*n^4 + (56/3)*n^3 + (121/3)*n^2 - (5/3)*n + 2
n=5: [linear recurrence of order 10; also a polynomial of degree 5 plus a quasipolynomial of degree 3 with period 2]
n=6: a(n) = (1987/180)*n^6 + (2033/30)*n^5 + (2785/18)*n^4 + 226*n^3 - (3017/180)*n^2 + (697/30)*n
n=7: [order 14; also a polynomial of degree 7 plus a quasipolynomial of degree 5 with period 2]

A255545 Lucky / Unlucky array: Each row starts with n-th lucky number, followed by all unlucky numbers removed at stage n of the sieve.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 6, 11, 19, 9, 8, 17, 39, 27, 13, 10, 23, 61, 57, 45, 15, 12, 29, 81, 91, 97, 55, 21, 14, 35, 103, 121, 147, 117, 85, 25, 16, 41, 123, 153, 199, 181, 177, 109, 31, 18, 47, 145, 183, 253, 243, 277, 225, 139, 33, 20, 53, 165, 217, 301, 315, 369, 345, 295, 157, 37, 22, 59, 187, 247, 351, 379, 471, 465, 447, 325, 175, 43

Offset: 1

Antti Karttunen, Feb 25 2015

The array A(row,col) is read by antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

			The top left corner of the array:
   1,   2,   4,   6,   8,  10,  12,   14,   16,   18,   20,   22,   24,   26,   28
   3,   5,  11,  17,  23,  29,  35,   41,   47,   53,   59,   65,   71,   77,   83
   7,  19,  39,  61,  81, 103, 123,  145,  165,  187,  207,  229,  249,  271,  291
   9,  27,  57,  91, 121, 153, 183,  217,  247,  279,  309,  343,  373,  405,  435
  13,  45,  97, 147, 199, 253, 301,  351,  403,  453,  507,  555,  609,  661,  709
  15,  55, 117, 181, 243, 315, 379,  441,  505,  571,  633,  697,  759,  825,  889
  21,  85, 177, 277, 369, 471, 567,  663,  757,  853,  949, 1045, 1141, 1239, 1333
  25, 109, 225, 345, 465, 589, 705,  829,  945, 1063, 1185, 1305, 1423, 1549, 1669
  31, 139, 295, 447, 603, 765, 913, 1075, 1227, 1377, 1537, 1689, 1843, 1999, 2155
  33, 157, 325, 493, 667, 835, 999, 1177, 1347, 1513, 1687, 1861, 2029, 2205, 2367
...

Inverse: A255546.
Transpose: A255547.
Column 1: A000959. Other columns of array as in A255543, e.g. column 2: A219178.
Row 1: A004275 (starting from 1).
See A255551 for a slightly different variant.

(define (A255545 n) (A255545bi (A002260 n) (A004736 n)))
(define (A255545bi row col) (if (= 1 col) (A000959 row) (A255543bi row (- col 1))))
;; Other code as in A255543.

For col = 1, A(row,col) = A000959(row); otherwise, A(row,col) = A255543(row,col-1).

A269606 T(n,k)=Number of length-n 0..k arrays with no repeated value differing from the previous repeated value by one or less.

Original entry on oeis.org

2, 3, 4, 4, 9, 6, 5, 16, 24, 8, 6, 25, 60, 62, 10, 7, 36, 120, 222, 154, 12, 8, 49, 210, 572, 804, 376, 14, 9, 64, 336, 1220, 2692, 2878, 902, 16, 10, 81, 504, 2298, 7030, 12570, 10192, 2142, 18, 11, 100, 720, 3962, 15630, 40288, 58280, 35812, 5040, 20, 12, 121

Offset: 1

R. H. Hardin, Mar 01 2016

Table starts
..2.....3......4.......5........6.........7.........8..........9.........10
..4.....9.....16......25.......36........49........64.........81........100
..6....24.....60.....120......210.......336.......504........720........990
..8....62....222.....572.....1220......2298......3962.......6392.......9792
.10...154....804....2692.....7030.....15630.....31024......56584......96642
.12...376...2878...12570....40288....105892....242226.....499798.....952180
.14...902..10192...58280...229754....714874...1886252....4405772....9366790
.16..2142..35812..268704..1304934...4811578..14654952...38768412...92013754
.18..5040.125012.1233046..7385898..32300252.113629480..340600002..902743646
.20.11786.434110.5636046.41679780.216337084.879470154.2988094770.8846649136

			Some solutions for n=6 k=4
..1. .0. .3. .0. .3. .2. .1. .1. .0. .3. .2. .3. .2. .1. .1. .2
..3. .2. .2. .2. .0. .4. .2. .2. .3. .4. .0. .0. .0. .4. .1. .2
..0. .0. .3. .4. .3. .2. .3. .3. .1. .4. .4. .3. .3. .3. .2. .3
..4. .1. .0. .3. .1. .0. .3. .1. .0. .3. .1. .1. .3. .0. .1. .1
..3. .3. .2. .4. .3. .4. .0. .0. .1. .4. .2. .3. .2. .3. .2. .0
..1. .3. .1. .3. .0. .4. .1. .3. .1. .0. .3. .3. .0. .3. .0. .0

R. H. Hardin, Table of n, a(n) for n = 1..9999

Column 1 is A004275(n+1).
Column 3 is A269532.
Row 1 is A000027(n+1).
Row 2 is A000290(n+1).
Row 3 is A007531(n+2).

Empirical for column k:
k=1: a(n) = 2*a(n-1) -a(n-2)
k=2: a(n) = 5*a(n-1) -5*a(n-2) -8*a(n-3) +12*a(n-4)
k=3: a(n) = 7*a(n-1) -9*a(n-2) -23*a(n-3) +31*a(n-4) +33*a(n-5)
k=4: [order 7]
k=5: [order 7]
k=6: [order 9]
k=7: [order 9]
Empirical for row n:
n=1: a(n) = n + 1
n=2: a(n) = n^2 + 2*n + 1
n=3: a(n) = n^3 + 3*n^2 + 2*n
n=4: a(n) = n^4 + 4*n^3 + 4*n^2 - n
n=5: a(n) = n^5 + 5*n^4 + 7*n^3 - 4*n^2 + n
n=6: a(n) = n^6 + 6*n^5 + 11*n^4 - 8*n^3 + n^2 + 3*n - 2
n=7: a(n) = n^7 + 7*n^6 + 16*n^5 - 12*n^4 - 5*n^3 + 18*n^2 - 15*n + 4

A204517 Square root of floor[A055859(n)/7].

Original entry on oeis.org

0, 0, 0, 1, 3, 6, 17, 48, 96, 271, 765, 1530, 4319, 12192, 24384, 68833, 194307, 388614, 1097009, 3096720, 6193440, 17483311, 49353213, 98706426, 278635967, 786554688, 1573109376, 4440692161, 12535521795, 25071043590, 70772438609, 199781794032, 399563588064

Offset: 1

M. F. Hasler, Jan 15 2012

nonn

M. F. Hasler, Truncated squares, OEIS wiki, Jan 16 2012
Index to sequences related to truncating digits of squares.

See also A031149=sqrt(A023110) (base 10), A204502=sqrt(A204503) (base 9), A204514=sqrt(A055872) (base 8), A204516=sqrt(A055859) (base 7), A204518=sqrt(A055851) (base 6), A204520=sqrt(A055812) (base 5), A004275=sqrt(A055808) (base 4), A001075=sqrt(A055793) (base 3), A001541=sqrt(A055792) (base 2).

b=7;for(n=1,2e9,issquare(n^2\b) & print1(sqrtint(n^2\b),","))

A204517(n)=polcoeff((x^4 + 3*x^5 + 6*x^6 + x^7)/(1 - 16*x^3 + x^6+O(x^n)),n)

A204517(n) = sqrt(floor(A204516(n)^2/7)).

G.f. = (x^4 + 3*x^5 + 6*x^6 + x^7)/(1 - 16*x^3 + x^6)

A207391 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 1 0 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 8, 14, 81, 98, 64, 10, 21, 196, 271, 200, 100, 12, 31, 441, 834, 643, 350, 144, 14, 46, 961, 2307, 2356, 1271, 556, 196, 16, 68, 2116, 6115, 7561, 5348, 2239, 826, 256, 18, 100, 4624, 16544, 23071, 19319, 10570, 3641, 1168, 324, 20, 147

Offset: 1

R. H. Hardin Feb 17 2012

Table starts
..2...4....6....9....14.....21.....31......46.......68......100.......147
..4..16...36...81...196....441....961....2116.....4624....10000.....21609
..6..36...98..271...834...2307...6115...16544....44250...116526....307117
..8..64..200..643..2356...7561..23071...72410...223804...678174...2060069
.10.100..350.1271..5348..19319..65955..232892...806886..2731598...9282799
.12.144..556.2239.10570..42167.158217..616386..2348280..8718366..32527713
.14.196..826.3641.18972..82477.335915.1424240..5887228.23664574..95673277
.16.256.1168.5581.31710.148743.651531.2975974.13215696.56972122.247183399

			Some solutions for n=4 k=3
..1..0..0....0..0..0....0..1..1....1..1..1....1..1..1....1..0..1....1..0..1
..0..0..0....0..1..1....1..1..0....1..1..1....1..0..1....1..0..1....0..1..1
..1..0..0....0..1..1....1..1..1....1..1..1....1..1..1....1..0..1....0..1..1
..0..0..0....0..1..1....1..1..1....1..1..1....1..1..1....1..0..1....0..1..1

R. H. Hardin, Table of n, a(n) for n = 1..480

Column 1 is A004275(n+1)
Column 2 is A016742
Column 3 is A207106
Column 4 is A207107
Row 1 is A038718(n+2)
Row 2 is A207069

Empirical for column k:
k=1: a(n) = 2*n
k=2: a(n) = 4*n^2
k=3: a(n) = (4/3)*n^3 + 8*n^2 - (10/3)*n
k=4: a(n) = (5/12)*n^4 + (13/2)*n^3 + (115/12)*n^2 - (17/2)*n + 1
k=5: a(n) = (2/15)*n^5 + (55/12)*n^4 + (101/6)*n^3 + (5/12)*n^2 - (299/30)*n + 2
k=6: a(n) = (1/36)*n^6 + (113/60)*n^5 + (151/9)*n^4 + (95/4)*n^3 - (605/36)*n^2 - (229/30)*n + 3
k=7: a(n) = (1/210)*n^7 + (103/180)*n^6 + (197/20)*n^5 + (1439/36)*n^4 + (293/20)*n^3 - (3469/90)*n^2 + (157/105)*n + 3

cp's OEIS Frontend

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A091090 In binary representation: number of editing steps (delete, insert, or substitute) to transform n into n + 1.

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A204520 Numbers such that floor(a(n)^2 / 5) is a square.

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A046698 a(0) = 0, a(1) = 1, a(n) = a(a(n-1)) + a(a(n-2)) if n > 1.

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A249982 T(n,k) is the number of length n+1 0..2*k arrays with the sum of the absolute values of adjacent differences equal to n*k.

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A255545 Lucky / Unlucky array: Each row starts with n-th lucky number, followed by all unlucky numbers removed at stage n of the sieve.

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A249982 T(n,k) is the number of length n+1 0..2k arrays with the sum of the absolute values of adjacent differences equal to nk.