A152198 -id:A152198 - cp's OEIS frontend

A152201 Triangle read by rows, A000012 * A152198.

1, 2, 3, 1, 4, 2, 5, 4, 1, 6, 6, 2, 7, 9, 5, 1, 8, 12, 8, 2, 9, 16, 14, 6, 1, 10, 20, 20, 10, 2, 11, 25, 30, 20, 7, 1, 12, 30, 40, 30, 12, 2, 13, 36, 55, 50, 27, 8, 1

Offset: 0

Gary W. Adamson, Nov 29 2008

Row sums = A027383: (1, 2, 4, 6, 10, 14, 22, 30,...).

			First few rows of the triangle =
1;
2;
3, 1;
4, 2;
5, 4, 1;
6, 6, 2;
7, 9, 5, 1;
8, 12, 8, 2;
9, 16, 14, 6, 1;
10, 10, 20, 20, 2;
11, 25, 30, 20, 7, 1;
12, 30, 40, 30, 12, 2;
13, 36, 55, 50, 27, 8, 1;
...

A152198, A027383

A000012 * A152198 = partial sums of A152198 column terms.

A207974 Triangle related to A152198.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 4, 2, 2, 1, 1, 5, 2, 4, 1, 1, 1, 6, 3, 6, 3, 2, 1, 1, 7, 3, 9, 3, 5, 1, 1, 1, 8, 4, 12, 6, 8, 4, 2, 1, 1, 9, 4, 16, 6, 14, 4, 6, 1, 1, 1, 10, 5, 20, 10, 20, 10, 10, 5, 2, 1

Offset: 0

Philippe Deléham, Feb 22 2012

Row sums are A027383(n).
Diagonal sums are alternately A014739(n) and A001911(n+1).
The matrix inverse starts
1;
-1,1;
1,-2,1;
1,-1,-1,1;
-1,2,0,-2,1;
-1,1,2,-2,-1,1;
1,-2,-1,4,-1,-2,1;
1,-1,-3,3,3,-3,-1,1;
-1,2,2,-6,0,6,-2,-2,1;
-1,1,4,-4,-6,6,4,-4,-1,1;
1,-2,-3,8,2,-12,2,8,-3,-2,1;
apparently related to A158854. - R. J. Mathar, Apr 08 2013
From Gheorghe Coserea, Jun 11 2016: (Start)
T(n,k) is the number of terms of the sequence A057890 in the interval [2^n,2^(n+1)-1] having binary weight k+1.
T(n,k) = A007318(n,k) (mod 2) and the number of odd terms in row n of the triangle is 2^A000120(n).
(End)

			Triangle begins :
n\k  [0] [1] [2] [3] [4] [5] [6] [7] [8] [9]
[0]  1;
[1]  1,  1;
[2]  1,  2,  1;
[3]  1,  3,  1,  1;
[4]  1,  4,  2,  2,  1;
[5]  1,  5,  2,  4,  1,  1;
[6]  1,  6,  3,  6,  3,  2,  1;
[7]  1,  7,  3,  9,  3,  5,  1,  1;
[8]  1,  8,  4,  12, 6,  8,  4,  2,  1;
[9]  1,  9,  4,  16, 6,  14, 4,  6,  1,  1;
[10] ...

Gheorghe Coserea, Rows n = 0..200, flattened

Cf. Columns : A000012, A000027, A004526, A002620, A008805, A006918, A058187
Cf. Diagonals : A000012, A000034, A052938, A097362
Cf. A007318, A110813, A135278, A152201
Related to thickness: A000120, A027383, A057890, A274036.

A207974 := proc(n,k)
    if k = 0 then
        1;
    elif k < 0 or k > n then
        0 ;
    else
        procname(n-1,k-1)-(-1)^k*procname(n-1,k) ;
    end if;
end proc: # R. J. Mathar, Apr 08 2013

seq(N) = {
  my(t = vector(N+1, n, vector(n, k, k==1 || k == n)));
  for(n = 2, N+1, for (k = 2, n-1,
      t[n][k] = t[n-1][k-1] + (-1)^(k%2)*t[n-1][k]));
  return(t);
};
concat(seq(10))  \\ Gheorghe Coserea, Jun 09 2016

P(n) = ((2+x+(n%2)*x^2) * (1+x^2)^(n\2) - 2)/x;
concat(vector(11, n, Vecrev(P(n-1)))) \\ Gheorghe Coserea, Mar 14 2017

T(n,k) = T(n-1,k-1) - (-1)^k*T(n-1,k), k>0 ; T(n,0) = 1.
T(2n,2k) = T(2n+1,2k) = binomial(n,k) = A007318(n,k).
T(2n+1,2k+1) = A110813(n,k).
T(2n+2,2k+1) = 2*A135278(n,k).
T(n,2k) + T(n,2k+1) = A152201(n,k).
T(n,2k) = A152198(n,k).
T(n+1,2k+1) = A152201(n,k).
T(n,k) = T(n-2,k-2) + T(n-2,k).
T(2n,n) = A128014(n+1).
T(n,k) = card {p, 2^n <= A057890(p) <= 2^(n+1)-1 and A000120(A057890(p)) = k+1}. - Gheorghe Coserea, Jun 09 2016
P_n(x) = Sum_{k=0..n} T(n,k)*x^k = ((2+x+(n mod 2)*x^2)*(1+x^2)^(n\2) - 2)/x. - Gheorghe Coserea, Mar 14 2017

A134816 Padovan's spiral numbers.

Original entry on oeis.org

1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, 351, 465, 616, 816, 1081, 1432, 1897, 2513, 3329, 4410, 5842, 7739, 10252, 13581, 17991, 23833, 31572, 41824, 55405, 73396, 97229, 128801, 170625, 226030, 299426, 396655

Offset: 1

Omar E. Pol, Nov 13 2007

a(n) is the length of the edge of the n-th equilateral triangle in the Padovan triangle spiral.
Partial sums of A000931. - Juri-Stepan Gerasimov, Jul 17 2009
Rising diagonal sums of triangle A152198. - John Molokach, Jul 09 2013
a(n) is the number of pairs of rabbits living at month n with the following rules: a pair of rabbits born in month n begins to procreate in month n + 2, procreates again in month n + 3, and dies at the end of this month (each pair therefore gives birth to 2 pairs); the first pair is born in month 1. - Robert FERREOL, Oct 16 2017

			a(6)=3 because 6+4=10 and A000931(10)=3.
G.f. = x + x^2 + x^3 + 2*x^4 + 2*x^5 + 3*x^6 + 4*x^7 + 5*x^8 + 7*x^9 + ... - _Michael Somos_, Jan 01 2019

Muniru A Asiru, Table of n, a(n) for n = 1..1500
J.-L. Baril, Avoiding patterns in irreducible permutations, Discrete Mathematics and Theoretical Computer Science, Vol. 17, No. 3 (2016).
Eric Fernando Bravo, On concatenations of Padovan and Perrin numbers, Math. Commun. (2023) Vol 28, 105-119.
Alain Faisant, On the Padovan sequence, arXiv:1905.07702 [math.NT], 2019.
Ed Harris, Pete McPartlan and Brady Haran, The Plastic Ratio, Numberphile video (2019).
Mariana Nagy, Simon R. Cowell, and Valeriu Beiu, On the Construction of 3D Fibonacci Spirals, Mathematics (2024) Vol. 12, No. 2, 201.
Christian Richter, Tilings of convex polygons by equilateral triangles of many different sizes, Discrete Mathematics 343.3 (2020): 111745. (See Section 2.1.)
Yuksel Soykan, Vedat Irge, and Erkan Tasdemir, A Comprehensive Study of K-Circulant Matrices Derived from Generalized Padovan Numbers, Asian Journal of Probability and Statistics 26 (12):152-70, (2024). See p. 154.
S. J. Tedford, Combinatorial identities for the Padovan numbers, Fib. Q., 57:4 (2019), 291-298.
Wikipedia, Padovan triangles
Index entries for linear recurrences with constant coefficients, signature (0,1,1).

The following are basically all variants of the same sequence: A000931, A078027, A096231, A124745, A133034, A134816, A164001, A182097, A228361 and probably A020720. However, each one has its own special features and deserves its own entry.

Cf. A060006.

a:=[1,1,1];; for n in [4..50] do a[n]:=a[n-2]+a[n-3]; od; a; # Muniru A Asiru, Aug 12 2018

a:=proc(n, p, q) option remember:
if n<=p then 1
elif n<=q then a(n-1, p, q)+a(n-p, p, q)
else add(a(n-k, p, q), k=p..q) fi end:
seq(a(n, 2, 3), n=0..100); # Robert FERREOL, Oct 16 2017

Drop[ CoefficientList[ Series[(1 - x^2)/(1 - x^2 - x^3), {x, 0, 52}], x], 5] (* Robert G. Wilson v, Sep 30 2009 *)
a[n_]=Round[Root[23#^3-5#-1&,1]Root[#^3-#-1&,1]^n ];a[Range[100]] (* OR *)
LinearRecurrence[{0, 1, 1}, {1, 1, 1}, 100] (* Federico Provvedi, Feb 12 2025 *)

{a(n) = if( n>=0, polcoeff( (x + x^2) / (1 - x^2 - x^3) + x * O(x^n), n), polcoeff( (x + x^2) / (1 + x - x^3) + x * O(x^-n), -n))}; /* Michael Somos, Jan 01 2019 */

my(x='x+O('x^50)); Vec(x*(1+x)/(1-x^2-x^3)) \\ Joerg Arndt, Feb 07 2025

a(n) = A000931(n+4).
G.f.: x * (1 + x) / (1 - x^2 - x^3) = x / (1 - x / (1 - x^2 / (1 + x / (1 - x / (1 + x))))). - Michael Somos, Jan 03 2013
a(1)=a(2)=a(3)=1, a(n) = a(n-2) + a(n-3) for n > 3. - Robert FERREOL, Oct 16 2017
a(n) = round(x*rho^n), where the Silver constant rho = Limit_{n->oo} a(n+1)/a(n) = A060006, and x is the real solution of the cubic 23*x^3-5*x-1 = 0. - Federico Provvedi, Feb 12 2025

More terms from Robert G. Wilson v, Sep 30 2009

First comment clarified by Omar E. Pol, Aug 12 2018

A152815 Triangle T(n,k), read by rows given by [1,0,-1,0,0,0,0,0,0,...] DELTA [0,1,-1,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.

Original entry on oeis.org

1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 1, 2, 1, 0, 0, 0, 1, 3, 3, 1, 0, 0, 0, 1, 3, 3, 1, 0, 0, 0, 0, 1, 4, 6, 4, 1, 0, 0, 0, 0, 1, 4, 6, 4, 1, 0, 0, 0, 0, 0, 1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0, 1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0, 0, 1, 6, 15, 20, 15, 6, 1, 0, 0, 0, 0, 0, 0, 1, 6, 15, 20, 15, 6, 1, 0, 0, 0

Offset: 0

Philippe Deléham, Dec 13 2008

Triangle read by rows, Pascal's triangle (A007318) rows repeated.

Riordan array (1/(1-x), x^2/(1-x^2)). - Philippe Deléham, Feb 27 2012

			Triangle begins:
  1;
  1, 0;
  1, 1, 0;
  1, 1, 0, 0;
  1, 2, 1, 0, 0;
  1, 2, 1, 0, 0, 0;
  1, 3, 3, 1, 0, 0, 0;
  1, 3, 3, 1, 0, 0, 0, 0;
  1, 4, 6, 4, 1, 0, 0, 0, 0; ...

Reinhard Zumkeller, Rows n = 0..150 of triangle, flattened

Cf. A007318, A064861, A152198 (another version), A000931 (diagonal sums), A016116 (row sums).

a152815 n k = a152815_tabl !! n !! k
a152815_row n = a152815_tabl !! n
a152815_tabl = [1] : [1,0] : t [1,0] where
   t ys = zs : zs' : t zs' where
     zs' = zs ++ [0]; zs = zipWith (+) ([0] ++ ys) (ys ++ [0])
-- Reinhard Zumkeller, Feb 28 2012

m = 13;
(* DELTA is defined in A084938 *)
DELTA[Join[{1, 0, -1}, Table[0, {m}]], Join[{0, 1, -1}, Table[0, {m}]], m] // Flatten (* Jean-François Alcover, Feb 19 2020 *)
T[n_, k_] := If[n<0, 0, Binomial[Floor[n/2], k]]; (* Michael Somos, Oct 01 2022 *)

{T(n, k) = if(n<0, 0, binomial(n\2, k))}; /* Michael Somos, Oct 01 2022 */

T(n,k) = T(n-1,k) + ((1+(-1)^n)/2)*T(n-1,k-1).
G.f.: (1+x)/(1-(1+y)*x^2).
Sum_{k=0..n} T(n,k)*x^k = A000012(n), A016116(n), A108411(n), A213173(n), A074872(n+1) for x = 0,1,2,3,4 respectively. - Philippe Deléham, Nov 26 2011, Apr 22 2013

Example corrected by Philippe Deléham, Dec 13 2008

A051163 Sequence is defined by property that (a0,a1,a2,a3,...) = binomial transform of (a0,a0,a1,a1,a2,a2,a3,a3,...).

Original entry on oeis.org

1, 2, 5, 12, 30, 76, 194, 496, 1269, 3250, 8337, 21428, 55184, 142376, 367916, 952000, 2466014, 6393372, 16586678, 43054344, 111801908, 290412296, 754543052, 1960808160, 5096293794, 13247503540, 34440553562, 89549255592, 232868582328, 605646682144

Offset: 0

Jonas Wallgren

Equals the self-convolution of A027826. Also equals antidiagonal sums of symmetric square array A100936. - Paul D. Hanna, Nov 22 2004

Equals eigensequence of triangle A152198. - Gary W. Adamson, Nov 28 2008

Alois P. Heinz, Table of n, a(n) for n = 0..1000
N. J. A. Sloane, Transforms

Cf. A051164, A051165, A051166, A027826, A100936, A100937, A152198.

a:= proc(n) option remember; add(`if`(k<2, 1,
      a(iquo(k, 2)))*binomial(n, k), k=0..n)
    end:
seq(a(n), n=0..40);  # Alois P. Heinz, Jul 08 2015

a[n_] := a[n] = 1 + Sum[Binomial[k, j]*Binomial[n-k, j]*a[j], {k, 1, n}, {j, 0, n-k}]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Nov 11 2015 *)

a(n)=1+sum(k=1,n,sum(j=0,n-k,binomial(k,j)*binomial(n-k,j)*a(j)))

a(n)=local(A,m); if(n<0,0,m=1; A=1+O(x); while(m<=n,m*=2; A=subst(A,x,(x/(1-x))^2)/(1-x)); polcoeff(A^2,n))
for(n=0,40,print1(a(n),", ")) \\ Paul D. Hanna, Nov 22 2004

a(n) = 1 + Sum_{k=1..n} Sum_{j=0..n-k} C(k, j)*C(n-k, j)*a(j). - Paul D. Hanna, Nov 22 2004
G.f. A(x) satisfies: A(x) = A(x^2/(1-x)^2)/(1-x)^2 and A(x^2) = A(x/(1+x))/(1+x)^2. - Paul D. Hanna, Nov 22 2004
a(0) = 1; a(n) = Sum_{k=0..floor(n/2)} binomial(n+1,2*k+1) * a(k). - Ilya Gutkovskiy, Apr 07 2022

More terms from Vladeta Jovovic, Jul 26 2002

A152828 Triangle read by rows, A007318 rows repeated three times .

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 4, 6, 4, 1, 1, 4, 6, 4, 1, 1, 5, 10, 10, 5, 1, 1, 5, 10, 10, 5, 1, 1, 5, 10, 10, 5, 1, 1, 6, 15, 20, 15, 6, 1, 1, 6, 15, 20, 15, 6, 1, 1, 6, 15, 20, 15, 6, 1, 1, 7, 21, 35, 35, 21, 7, 1, 1, 7, 21

Offset: 0

Philippe Deléham, Dec 13 2008

Diagonal sums : A079398 . Lengths of row are : 1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,... (A008620) .

			Triangle begins : 1 ; 1 ; 1 ; 1,1 ; 1,1 ; 1,1 ; 1,2,1 ; 1,2,1 ; 1,2,1 ; 1,3,3,1 ; 1,3,3,1 ; 1,3,3,1 ; 1,4,6,4,1 ; ...

Cf. A007318, A152198, A152815

{#,#,#}&/@Table[Binomial[n,k],{n,0,11},{k,0,n}]//Flatten (* Harvey P. Dale, Jul 22 2024 *)

A152830 Triangle read by rows, A007318 rows repeated four times .

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 4, 6, 4, 1, 1, 4, 6, 4, 1, 1, 4, 6, 4, 1, 1, 5, 10, 10, 5, 1, 1, 5, 10, 10, 5, 1, 1, 5, 10, 10, 5, 1, 1, 5, 10, 10, 5, 1, 1, 6, 15, 20, 15, 6, 1, 1, 6, 15, 20, 15, 6, 1, 1

Offset: 0

Philippe Deléham, Dec 13 2008

Diagonal sums : A103372 .

			Triangle begins : 1 ; 1 ; 1 ; 1 ; 1,1 ; 1,1 ; 1,1 ; 1,1 ; 1,2,1 ; 1,2,1 ; 1,2,1 ; 1,2,1 ; 1,3,3,1 ; ...

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Cf. A007318, A152198, A152815, A152828.

Flatten[Table[#,{4}]&/@Table[Binomial[n,k],{n,0,6},{k,0,n}]] (* Harvey P. Dale, Sep 23 2015 *)

A152831 Triangle read by rows, A007318 repeated five times .

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 4, 6, 4, 1, 1, 4, 6, 4, 1, 1, 4, 6, 4, 1, 1, 4, 6, 4, 1, 1, 5, 10, 10, 5, 1, 1, 5, 10, 10, 5, 1, 1, 5, 10, 10, 5, 1, 1, 5, 10, 10, 5, 1, 1, 5

Offset: 0

Philippe Deléham, Dec 13 2008

Diagonal sums : A103373 .

			Triangle begins : 1 ; 1 ; 1 ; 1 ; 1 ; 1,1 ; 1,1 ; 1,1 ; 1,1 ; 1,1 ; 1,2,1 ; 1,2,1 ; 1,2,1 ; 1,2,1 ; 1,2,1 ; 1,3,3,1 ; ...

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Cf. A007318, A152198, A152815, A152828, A152830.

Flatten[Table[#, {5}] & /@ Table[Binomial[n, k], {n,0,10}, {k, 0, n}]] (* G. C. Greubel, May 03 2017 *)

A152844 Triangle read by rows, A007318 rows repeated six times .

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 4, 6, 4, 1, 1, 4, 6, 4, 1, 1, 4, 6, 4, 1, 1, 4, 6, 4, 1, 1, 4, 6, 4, 1, 1, 5, 10, 10, 5, 1, 1, 5, 10, 10, 5, 1, 1

Offset: 0

Philippe Deléham, Dec 14 2008

Diagonal sums : A103374 .

			Triangle begins : 1 ; 1 ; 1 ; 1 ; 1 ; 1 ; 1,1 ; 1,1 ; 1,1 ; 1,1 ; 1,1 ; 1,1 ; 1,2,1 ; 1,2,1 ; 1,2,1 ; 1,2,1 ; 1,2,1 ; 1,2,1 ; 1,3,3,1 ; ...

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Cf. A007318, A152198, A152815, A152828, A152830, A152831.

Flatten[Table[#, {6}] & /@ Table[Binomial[n, k], {n,0,10}, {k, 0, n}]] (* G. C. Greubel, May 03 2017 *)

A152845 Triangle read by rows, A007318 rows repeated seven times .

Original entry on oeis.org

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

Offset: 0

Philippe Deléham, Dec 14 2008

Diagonal sums : A103375 .

			Triangle begins : 1 ; 1 ; 1 ; 1 ; 1 ; 1 ; 1 ; 1,1 ; 1,1 ; 1,1 ; 1,1 ; 1,1 ; 1,1 ; 1,1 ; 1,2,1 ; 1,2,1 ; 1,2,1 ; 1,2,1 ; 1,2,1 ; 1,2,1 ; 1,2,1 ; 1,3,3,1 ; ...

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Cf. A007318, A152198, A152815, A152828, A152830, A152831, A152844

Flatten[Table[#, {7}] & /@ Table[Binomial[n, k], {n, 0, 10}, {k, 0, n}]] (* G. C. Greubel, May 03 2017 *)

cp's OEIS Frontend

A152201 Triangle read by rows, A000012 * A152198.

Views

Author

Keywords

Comments

Examples

Crossrefs

Formula

A207974 Triangle related to A152198.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

PARI

PARI

Formula

A134816 Padovan's spiral numbers.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

GAP

Maple

Mathematica

PARI

PARI

Formula

Extensions

A152815 Triangle T(n,k), read by rows given by [1,0,-1,0,0,0,0,0,0,...] DELTA [0,1,-1,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Mathematica

PARI

Formula

Extensions

A051163 Sequence is defined by property that (a0,a1,a2,a3,...) = binomial transform of (a0,a0,a1,a1,a2,a2,a3,a3,...).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI

PARI

Formula

Extensions

A152828 Triangle read by rows, A007318 rows repeated three times .

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A152830 Triangle read by rows, A007318 rows repeated four times .

Views

Author

Keywords

Comments