A134148 -id:A134148 - cp's OEIS frontend

A160711 Cyclops squares: squares (A000290) that are also cyclops numbers (A134808).

0, 11025, 19044, 21025, 24025, 32041, 38025, 42025, 47089, 51076, 58081, 59049, 65025, 66049, 67081, 75076, 87025, 93025, 1110916, 1140624, 1170724, 1190281, 1240996, 1270129, 1290496, 1340964, 1350244, 1380625, 1420864, 1430416

Offset: 1

Omar E. Pol, Jun 08 2009

			19044 is in the sequence because it is a square (138^2) and is also a cyclops number (odd number of digits, middle digit is the only zero).
11025 is in the sequence because it is a square (105^2) and is also a cyclops number (odd number of digits, middle digit is the only zero). - _Michael B. Porter_, Jul 09 2016

Kenny Lau, Table of n, a(n) for n = 1..20001

Cf. A000290, A134808, A134809, A134148, A138131, A153806, A160712, A160717, A239828.

Select[Range[0, 1200]^2, And[OddQ@ Length@ #, #[[Ceiling[Length[#]/2]]] == 0, Count[#, 0] == 1] &@ IntegerDigits@ # &] (* Michael De Vlieger, Jul 08 2016 *)
cnQ[n_]:=Module[{len=IntegerLength[n]},OddQ[len]&&DigitCount[n,10,0]==1 && IntegerDigits[n][[(len+1)/2]]==0]; Join[{0},Select[Range[1200]^2,cnQ]] (* Harvey P. Dale, Mar 19 2018 *)

A134146 Triangle of numbers obtained from the partition array A134145.

Original entry on oeis.org

1, 3, 1, 15, 3, 1, 105, 24, 3, 1, 945, 150, 24, 3, 1, 10395, 1485, 177, 24, 3, 1, 135135, 14805, 1620, 177, 24, 3, 1, 2027025, 191520, 16425, 1701, 177, 24, 3, 1, 34459425, 2687580, 208125, 16830, 1701, 177, 24, 3, 1, 654729075, 44552025, 2880360, 212985

Offset: 1

Wolfdieter Lang, Nov 13 2007

This triangle is named S2(3)'.

In the same manner the unsigned Lah triangle A008297 is obtained from the partition array A130561.

			[1]; [3,1]; [15,3,1]; [105,24,3,1]; [945,150,24,3,1];...

W. Lang, First 10 rows and more.

Cf. A134147 (row sums).
Cf. A134148 (allternating row sums).
Cf. A134134 (k=2 member of this triangle family).

a(n,m)=sum(product(S2(3;j,1)^e(n,m,q,j),j=1..n),q=1..p(n,m)) if n>=m>=1, else 0. Here p(n,m)=A008284(n,m), the number of m parts partitions of n and e(n,m,q,j) is the exponent of j in the q-th m part partition of n. S2(3;j,1)= A001147(j) = A035342(j,1) = (2*j-1)!!.

A160712 Composite cyclops numbers (A134808).

Original entry on oeis.org

102, 104, 105, 106, 108, 201, 202, 203, 204, 205, 206, 207, 208, 209, 301, 302, 303, 304, 305, 306, 308, 309, 402, 403, 404, 405, 406, 407, 408, 501, 502, 504, 505, 506, 507, 508, 602, 603, 604, 605, 606, 608, 609, 702, 703, 704

Offset: 1

Omar E. Pol, Jun 08 2009

Cf. A134808, A134809, A134148, A138131, A153806, A160711, A160717.

Edited by Omar E. Pol, Jul 04 2009

A134147 Row sums of triangle A134146 and partition array A134145 (M3(3)/M3).

Original entry on oeis.org

1, 4, 19, 133, 1123, 12085, 151765, 2236876, 37373866, 702393424, 14611910794, 333811635793, 8298224157103, 223061783080075, 6444694333816630, 199168434836797921, 6555131451981351961, 228906927287899911709

Offset: 1

Wolfdieter Lang, Nov 13 2007

Cf. A000041, A134148 (alternating row sums of triangle A134146).

a(n) = Sum_{m=1..n} A134146(n,m), n>=1.

a(n) = Sum_{k=1..p(n)} A134145(n,k), with p(n) = A000041(n) (number of partitions of n).

cp's OEIS Frontend

A160711 Cyclops squares: squares (A000290) that are also cyclops numbers (A134808).

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A134146 Triangle of numbers obtained from the partition array A134145.

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A160712 Composite cyclops numbers (A134808).

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A134147 Row sums of triangle A134146 and partition array A134145 (M3(3)/M3).

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